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Fixing Today’s Education / Common Core Education – Blog Post 2

06 Jun

How do we fix it?

 

In the last blog post, I talked about a variety of things that were wrong in today’s educational system.  Specifically, we keep repeating our mistakes with the math curriculum and we don’t have consistency between schools in their interpretation of our new common core standards illustrating that if we can’t even get two schools in the same county to interpret the standards the same, how are multiple states and counties going to actually have consistency among the common core standards.  I also mentioned the inconsistency of grading among schools leading to grading standards that have no meaning.  Finally, I talked about both the inappropriate expectations of students and how these and other factors can lead students to have poor educational self-esteem.

So, the question becomes, how do we fix it?  Right now, educators seem to believe that fixing the U.S. education system lies in the curriculum.  They believe that if a bunch of smart Ph.D.’s gather together as a group and write a set of standards and provide those standards to the state, this will fix our educational problems.  Or at least, I am guessing this it as this has been the only solution we have ever employed to fix our educational system.  It hasn’t worked before and it won’t work this time either and I will tell you why.  Even if the curriculum is broken, which I believe it is, writing new curriculum and handing a concept that is developed by people who understand teaching / education at a higher level does not translate to implementation in the classroom.  The curriculum has to be implemented by teachers and the teachers are not properly educated and motivated to implement these new ideas.  We keep handing off these high level concepts to be taught by teachers who only know how to teach the way they have been already teaching.  We do not invest money in reeducating our teachers how to use this curriculum.  Our teachers weren’t taught this way and therefore are not going to just be able to shift gears and suddenly know how to teach conceptually when all they are given is a set of written standards.  In fact, many elementary math teachers (as well as some middle school and high school math teachers) lack the mathematical knowledge of these concepts to begin with.  They have procedural knowledge but lack true conceptual knowledge.  My dissertation for my Ph.D. looked at elementary school teacher’s conceptual understanding of statistical concepts that they were teaching and found a significant number of misconceptions and lack of understanding in their knowledge.

Our teacher education programs are very weak.  We do not spend enough time within our methods classes properly educating teachers  and sometimes methods classes are taught by college professors who lack the ability to teach preservice teachers how to teach anything but the traditional approach.  In reference to the new common core objectives, I was told that preservice teachers were told to make two lesson plans – one that used the “old” curriculum approach and a second lesson plan that employed the goals and objectives of common core mathematics.  The professor found no significant difference in the students’ lessons plans.  If this is happening while teachers are in a methods class that is supposed to be teaching them about how to implement the new common core standards, imagine how difficult it is for current teachers who only know how to teach the way their currently teach.

We all know that putting financial resources towards education is not a priority in our country.  However, if you look at where we spend money and don’t spend money, there are some major changes that could be made.  First, I know our state spends a significant amount of money on different assessments, software programs, and thinks that adding more school days (which costs money) will make our kids smarter.  If instead of spending money on these things, they focused money on and time on requiring more teacher inservice education on a regular basis from top educators who really understand how to implement this new common core curriculum, they would be much more successful in improving educational achievement.  It isn’t the students who need more time in school, it is the teachers.  These teachers need inservice training workshops on a regular basis, not just teacher workday – planning time.

In some countries, the teachers are held accountable for student learning.  We don’t do enough of that in our country.  So many teachers are complacent.  I hear about teachers giving tests where the average score on the test is in the 60’s.  If a test has an average score that low, then the teacher did something wrong.  Teachers don’t want to hold themselves accountable.  It is our job to make sure the students learn the material.  Granted, everyone can’t get A’s and B’s and I am not a believer in grade inflation but I am a believer in making sure that I provided the material in a way that all students who put forth effort could understand it and that my assessment was reasonable for the students.  If the test average is really low, then *I* didn’t do a good enough job with either teaching or making my assessment and *I* need to make changes.  *I* need to figure out if material needs to be retaught or if my test was inappropriate and I need to give a new test.  Additionally, *I* need to learn from this mistake so that this doesn’t happen repeatedly so that *I* become better at making sure my students are learning.  The responsibility is not all on the students, too many teachers forget that.

If we find some students who are consistently failing all their subjects despite being in good classes, our education system needs to jump in and do something for these students.  Our local high schools do nothing, these students just get passed along – either the teachers decide to give them a D at the end or they retake the classes they failed and their report cards look like a train wreck.  When we see this happening to a student in their freshman year, why are we noticing this but not stepping in and figuring out how we can help this student?  What is the job of our school counselors?  Should they be required to monitor the academic progress of students and provide needed intervention for those students who need it?

 

The big picture is this:  in order to fix our educational system, we need to:

  1. Provide more methods courses with better content to preservice teachers

  2. Provide and commit funding to regular inservice training so they can implement the common core standards the way they were intended

  3. Instead of adding more days for students in school, add more days for teachers for inservice training that focuses on implementing curriculum

  4. Make teachers accountable for their students’ learning to some extent

  5. Educate teachers how to create better tests for students

  6. Provide equality among schools in terms of content and grading practices

  7. Don’t just hand teachers a new curriculum and expect they can implement it

  8. Have teachers and counselors intervene with students who are not passing their classes early on in the semester / early school years (freshman year high school)

 

Support for my argument can be found at this link:  http://larrycuban.wordpress.com/2012/03/03/why-common-core-standards-will-fail-jay-mathews-and-chester-finn/

 

Coming Soon – Looking into Common Core Math for Elementary School

 
 

Why Wake County Public School will have poor EOG and EOC test scores with new Common Core

04 Jun

Dear Wake County Public Schools,

 

As an educator who has passionately dedicated myself to educating students, I am appalled at the lack of drive of many of WCPSS teachers (mostly middle and high school), the lack of organization of passing along information to schools and teachers from Central Office, and the inability to truly assess and provide for students.  Let me give some examples of what I see come into my learning center.

Example 1:  Quite a few teachers (from different schools) have been providing their students with review packets to prepare them for the Common Core Math 1 EOC.  All the problems in these packets are procedural problems and some are as simple as “What type of plot is this?”  Answer:  Dot Plot.  These teachers were obviously not informed at all about the nature of the new CCM1 EOC.  North Carolina released a practice test to help teachers get a feel for what the expectations will be on the test, however, obviously this practice test was not given to teachers.  The level of questions on the actual EOC for CCM1 is at such a higher level than most teachers are preparing their students.  The majority of the problems are multi-step  problems that often combine multiple concepts together.  A student who only practices isolated procedural knowledge will most likely not be prepared for this test unless they are naturally gifted in math.  In fact, the students who did the best on this practice EOC were the 7th graders who were advanced enough to be taking CCM1 in the 7th grade.

 

Example 2:  Test questions tend to focus on “how can we trick the student?”  After seeing the practice test and talking with teachers who have given the EOG’s, many of the questions specifically try to trick the reader.  The question might be set up to solve for x (after about 15 steps), however, if the student tires and after all that work, just selects (or writes for gridded response question) the answer they got for x, they may still get the question wrong because the question asked for some relationship to x, rather than x itself.  One teacher commented on how when she gave the practice EOG, she found 4 of these problems either to be trick questions or very challenging but thought, well, it is only 4 questions – but, upon giving the actual EOG, found the entire test to be like those 4 problems and saw her best math students falling in the “traps” set by the test makers.

 

Example 3:  I am just shocked at the inability for math teachers at the middle and high school level to accurately assess student knowledge.  I have students who clearly understand things at a reasonable level who are failing their math course while other students who are unable to do almost any math problem presented to them are being passed through by teachers who don’t want their grade roster to have too many F’s.  Teachers are showing students tests ahead of time so they can make sure they do okay, allowing them to take pictures of the tests and then work on them the next day. Another teacher who was told to pass a failing student, substituted a review homework (that was mostly likely not the independent work of the student to begin with) for all his missing test grades to bring his grade from a 38 to a 74 so he will pass the class.

 

Example 4:  Students are expected to be able to use technology at an appropriate level to be successful on the CCM1 EOC and some teachers just don’t teach much or any calculator work to students, this leaves them at a huge disadvantage.  Additionally, the idea that this curriculum is supposed to be “Common Core” is a joke, the variety of ways the content for CCM1 is taught is amazing, there have been no text books and each school has had very different approaches and content.  Many are missing content.  The EOC contains linear programming but not one teacher that I know taught linear programming to their CCM1 class.

 

The Common Core standards assumes a level of sophistication by teachers that they just don’t have.  The idea behind common core is to teach math with a conceptual understanding and the EOG’s and EOC’s certainly test for this with all application multi-step problems.  However, students are not being prepared in the classroom to meet these standards because the teachers are not able to teach at this level, are not provided with the resources, and are not able to accurately assess student knowledge.

In order for Common Core Mathematics in North Carolina to be successful, North Carolina needs to provide teachers with a lot more training on how they are supposed to teach, what they are supposed to teach, and provide common assessments in CCM1 for teachers like they do in elementary school so that teachers are all assessing at the same standards.  Teachers need to be held accountable for poor teaching, simply inflating the grade of a failing student does nothing but further promote the problems that we find down the road that North Carolina complains about!

 

 
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Fixing Today’s Education System: A look into the new Common Core Standards

12 Apr

Fixing Today’s Education System

Part 1:  Introduction

If you look at reports that compare the United States education to other developed countries, you will find that the U.S. is not highly ranked.  In mathematics, in particular, the U.S. is only ranked around 25th according to the Program for International Student Assessment that ranked 70 countries.  Why is our country failing our students in education?  What can we do to improve the future of education in the United States?

Although, I will address things broadly, I will put much of the focus on mathematics for two reasons.  First, it is the area that we are the worst at and it is the area that I am most qualified to address.  If you look at the most recent mathematical reform you see some general trends.  Schools were teaching math but decided that students were lacking concepts and thus changed the curriculum to a generation who learned under New Math.  New Math was supposed to do a better job at presenting concepts to students.  However, New Math seemed to fail and so the educators in high places deemed a new approach called, “Back to Basics.”  Back to Basics was an attempt at not confusing students too much with all these concepts New Math unleashed upon the children that were unsuccessful and instead encouraged students to focus on the basics of math – adding, subtracting, multiplying, and dividing.  However, after a while on this new approach, a new group of educators, yet again realized that students could do the procedural math but were again not really understanding the concepts and able to problem solve.  After Back to Basics was deemed a failure, the new push was to create a new curriculum of standards that was created by a group of math teachers from the National Council of Teachers of Mathematics who would write out specific goals that included both procedural and conceptual knowledge for students to grasp mathematics.  From the NCTM standards, states developed their own “Standard Course of Study” that would meet the NCTM standards and this was the new plan of action to make students successful in mathematics.  However, we continued to see problems with students in math and no real improvement in grades.  The educators now decided that there were too many differences across the states and again not enough conceptual understanding was being taught.  One state had one curriculum and another state had something completely different.  We needed a more cohesive curriculum across all states.  Not only that, we needed to get teachers to go back to making sure students can actually explain every math step they perform, being sure they understand the concept – in other words, more of a focus on conceptual understanding rather than procedural understanding (read New Math here.)  So, they created the Common Core Standards.  These new standards show each grade level what they should learn and give examples to those who read them about how to interpret different mathematical concepts that the standards want students to learn.  This is where we are at today.

If you look at the history and the big picture, you can see that we just keep doing the same thing.  Pushing our focus back and forth between procedural and conceptual knowledge.  Each time our plan doesn’t work, so we switch to the other focus and forget that we already tried this “idea” just in a different way.  The idea of having a common core for all states may sound “different,” but this common core has not been providing the common curriculum among schools in the same county, never mind within the same state as intended. I can only give examples from schools that I know but I would like to provide these as a way of illustrating how the idea of providing a document of “common core,” delivering it to each school provide an insufficient execution of the same content even within the same county..  I run a learning center and tutor children from many different schools.  This is the first semester our school system has offered Common Core Mathematics to students in its public schools.  Here is what I am observing.

 

School A:

Prior to common core, the course was Algebra 1 – it has since “changed” and now teachers should be implementing this new curriculum for Common Core 1.

Last Year in Algebra 1:  Students worked out of an old Algebra 1 textbook, teacher shows examples, students do homework, teacher gives tests, students are not allowed to use calculators, technology is not encouraged at all or used to teach concepts in Algebra.

This Year in Common Core 1:  NOTHING has changed, except, teachers are working at a slightly faster pace so they can add a couple new sections (worksheets) that are covered in common core during the last couple weeks of school relating to Geometry.  There is nothing different in how Common Core is being taught this year than the way they taught Algebra 1 last year.   Basically, it is the same course with 1-2 lessons of Geometry added in.

 

School B:

Prior to common core, the course was Algebra Part 1 and Part 2 – the teachers used an Algebra book and students worked through problems, took quizzes and tests often.  They used calculators as often as they wanted.  Students were often given 40 problems a night to reinforce the algebra concepts they were learning.  The topics fell in a nice sequencial pattern.  Teachers taught some technology but kids were allowed to use technology as much as they wanted to if they learned more on their own.

This year as Common Core 1:  Students are being taught out of worksheet packets that cover topics that more closely fit the Common Core topics.  The overall coverage of material is moving much slower and although students are getting taught material that better fits the curriculum, they are still not being encouraged to build concepts or practice as much as one would expect given the intent of the common core class.  However, overall School B has taken on the spirit much better than School A.  Students will often get homework with 3-4 problems to solve and this is insufficent to help them internilze the material and even work enough of a variety of different types of problems.  The glasses are very disorganzized and do a lot of discovery learning.  For some students who are smart, they may learn this way but the average student and definately the struggling student does not do well with discovery learning.  These students need examples, explanations, links and connections to things they already know, and sufficient practice on these topics.  This is not happening at this school.  Some times the students get tests and have to tell the teacher that the questions are asking things that he forgot to teach them.  There are no study guides, no direction, and not enough problems to prepare you for what is expected of you.

 You can see how different these two schools are and yet these students are taking the same course. Which is better?  Well, there are things that School A does better since it teaches math in an orderly fashion and gives enough homework for students to get the content.  However, they don’t spend time linking concepts (which the other school does).  They also don’t allow technology and the tests assume 60% calculative active, so students need to be strong in their ability to use calculators.  Overall, the kids are learning more but there areas of improvement – pulling out some wasted time on certain topics and use that time to cover other topics mentioned in the CCM1 standards.

 However, there are some things that school B does better.  They show students a lot of applications of linear, quadratic, and exponential models.  They spend a lot of time creating equations with various given information.  They ask thinking questions.  But, they do too much and the procedural knowledge gets lost and the student only ‘kind of” gets the conceptual knowledge being presented because it isn’t being linked to something they already knew.  They don’t have enough repetition and don’t do enough procedural knowledge.  The order of the material does not fit will which also impedes their ability to link key ideas for students.  They also will waste a week on a very easy topic but then rush through a hard topic in 2-3 days.  Students, overall, in school B are struggling more than in school A.

Here is another example.

 

4th grade School C:

Fourth graders in math at this school are being taught the topics stated in the common core curriculum.  Each week, they have to write journal entries that explain reasons behind what they do.  They have to be able to explain things like why a square is a rectangle but a rectangle is not a square in words.  They explore multiple ways to do different types of problems and then have to explain how they used their approach to get their answer.  The teachers ask, “why?” questions on tests and homework.  The teachers anticipate that the new End of Course tests will also be asking students open ended questions.

 

4th grade School D:

Students at this school, in the same town, are using the same homework book they used last year before common core.  They never get asked to explain any reasoning behind their work.  They simply do calculations and word problems.  The new thing the teacher added was word problems from an online web site the students log into at home.  Overall, there appears to be very little to no change in how this year’s material is taught compared to last year even though there is a whole new curriculum.

 

Another example of how much schools differ within the county goes even outside the common core concept.  Schools don’t even have the same grading rules, some schools are significantly harder than other schools, and some schools inflate grades.  All of this leads to the fact that an A, B, C – they have no meaning.  I had one student in Honors Geometry at this school that I think is a very harsh school for grading, get a C. He was very bright, he knew the concepts very well.  At any other school, he would have gotten an A.  His teachers just graded hard and gave really hard tests.  I had another student who got an A+ in Algebra 2 at one school who grades very easily and the classes in general are very easy.  It is a private school and I find this to be a trend.  It is almost as if you pay to get your child good grades.  Her knowledge in Algebra was poor but her grade was an A+.  All the children I know who struggle with grades in public school and then switch to these private schools start getting A’s and B’s.  I am not in the classroom and don’t see the tests, so I can’t judge but my point here is the overall inequity among grades in these schools.  Here is another example:  School A gives 0’s when a student doesn’t hand in work, this brings down grades significantly causing students to get poor grades.  Right down the road, School B says, “it is too hard to recover from a 0, so we will turn all 0’s to 50’s.”  Right there, is a huge difference in what a student’s score at School A and School B will be if they miss some assignments.  All of these grades are meaningless.  The only ones that count are on tests such as the AP exams or SAT’s where everyone takes the same test, however, I am not a fan on SAT questions as they don’t match up with what students actually learn in high school.  The math SAT questions are not traditional Algebra and Geometry questions, they are novel problem solving questions and some students who are good students, may just not have success on that type of test.  Additionally, the SAT verbal requires memorization of hundreds of vocabulary words to do well.  Many of these words are words that are very obscure and do not predict the success of a student. 

It isn’t just math where we see these large variations among school.  I was at an IEP meeting the other day and the first grade teacher told me how the child, a young boy, in her class needed help with writing.  I asked her about her expectations for writing in the first grade.  She told me they were writing persuasive essays and handed me a sheet that said he would need to have a topic sentence, use at least once complex sentence, have a sentence that uses some level of complex punctuation such as commas in a list of items, have descriptive words in his sentences in addition to correct spelling, punctuation, grammar, and there had to be an overall flow in the essay that showed one event following the other.  This is the very beginning of the second quarter of FIRST grade and he is a boy!  This was so developmentally inappropriate for this child to be expected to write a persuasive essay with all these expectations.  If a child of age 5 or 6 can even understand the concept of a persuasive essay, that would be an achievement!  Although, she was the most extreme example I have seen, many of the children who come to my center come in with 2’s (the grading system in our state is 1,2,3,4 and a 2 is that you are not performing at the expected level) because the expectations in writing in our state are just too high.  The children might have a chance of reaching these goals if teachers actually spent time teaching students grammar but they don’t.  Children come in expected to write complete essays with perfect sentences and with all these specific goals, however, they can’t tell me what a noun or a verb is.  Teachers, at least in my state, are just ignoring grammar altogether.  They don’t seem to think it is relevant to writing.  On top of that, the teachers have no idea how to teach writing.  They just have “expectations” that the students will do it.  So, the smart ones learn to figure it out on their own or get outside help and the others just crash and burn.  When my son was in fifth grade, the teachers were so focused on the enormous amount of social studies the state / school required they present to students that although my son couldn’t yet write a sentence, they felt that taking the time to do so was not as important as the time they needed for social studies.  I mentioned, at an IEP meeting, that he couldn’t spell either, and they told me that it didn’t matter because that is what spell checkers on computers were for.  It was appalling.  How many teachers give spelling tests to students and don’t care about the results?  When your child gets a word wrong on a spelling test, is anything ever done about it?  Do they revisit the word so that the child eventually learns to spell the word or is it just marked in a book and on they go?  How much time does the teacher put into picking out the words for a spelling list?  Again, I saw the difference between schools in this aspect.  I had my child at one school where the teacher picked completely random words that had no relationship to each other and weren’t even words that my child might use at his age.  Another school, the words were more appropriate, although still weren’t related to each other so that they helped teach a phonetic pattern to a child, although I have seen (through my center) a few good teachers give spelling lists with words that were well thought out, grouped according to sound patterns and age appropriate.  The variation, however, among spelling words is so inconsistent just as everything else.  My own daughter is very advanced in spelling and was doing 6th grade spelling words in 3rd grade.  When passed onto 4th grade, her new teacher had her repeat all the lessons she did in 3rd grade from the 6th grade spelling book (even though she got all 100’s in 3rd grade on the words), saying that review was good.  Actually, my feeling is that she was just too lazy to find lessons for her even though I offered to provide them.  So, I ask, what about the good spellers?  What about the weak spellers?  Shouldn’t we assess a child accurately (and do teachers know how to do this) and match their spelling lists to their actual level so they are learning appropriate information?

Children learn from building on what they already know.  If you jump too far ahead of what they know, they can’t make that leap and you will waste your time and their precious time teaching them things they aren’t ready for.  When children get behind in school but we fail to acknowledge that or make adjustments and just keep them with the rest of the class, they will only get further and further behind.  You can’t go from adding one digit numbers to subtraction with borrowing across zero.  You won’t make it.  You can’t take a reader who is comprehending at grade 2 and expect them to be successful in grade 3 or 4 just because you passed them along.  What does this do to our children?  The biggest problem I run across in my center is a students sense of themselves as a learner.  I call it their educational self-esteem.  When a child fails all the time, sees that 2 on their report card, or is the one who “just doesn’t get it” over and over, they begin to bring those thoughts into their sense of self.  They see themselves as a dumb person and this stays with them for life and impacts their future education because they will always figure, “they just can’t do it.”  When I taught undergraduate and graduate students, I would often ask them to write a math biographical essay about themselves.  I wanted them to tell me how they saw themselves as a learner in mathematics and what molded them to feel they way they do.  The majority of students who were non-math majors had negative math self-esteem.  They felt they weren’t good in math and never would be.  They often relayed stories of terrible events that happened such as teachers telling them they were stupid in front of the class and belittling them.  Others just got beaten down by the system of poor teaching and bad experiences.  After teaching my math classes with a “everyone can do this attitude,” and presenting material in a way that always leads to the “why couldn’t anyone have showed me this before?” question, my student’s attitude would change.  They would be shocked to learn that it was in them all along and they just needed someone to believe in them and teach in less traditional ways that allow for greater learning to take place.  We will talk about teaching techniques later on.  The point here is that all of these inappropriate expectations, all of these failing grades, and having teachers who don’t really want to be in the classroom for the right reasons provide children with negative educational self-esteem.  We need to break this cycle.

 

Next Blog:  How Do We Fix It?

Future Blogs:  Looking at the common core grade by grade

 
 

Accommodations for Students with Memory Problems in Mathematics

03 Feb

As the owner of The ALC Education Center in North Carolina, I see many students who have struggles in mathematics.  These struggles arise from a variety of issues.  Some of the most common reasons are:

1.  Their learning style does not match the teacher’s teaching style

2.  They have a slower processing speed and need more time to digest information than the average student

3.  They simply need additional explanations due to our poor educational system – unmotivated teachers who lack proper training and don’t teach math well

4.  Weak number sense

5.  Memory issues

I am going to discuss #5, Memory Issues, in this post.  If your son or daughter is the child who can do the math at the time it is presented but later when tested on the same information after a period of time appears to have “forgotten” the information, your child may have memory issues.  This is much more common than people realize.  He or she is the child that once you remind them once, can pull it out of their head and say, “oh…” and proceed to work through the problem without issue.  These students DO NOT have a problem working through problems during sessions that focus on those problems, they are able to get all the problems correct.  When asked about understanding of the concept, they seem to grasp the majority of the underlying idea.  However, although the information is stored in their brains, they cannot access it at will at a later date.  The problems they once did with ease, seem all new again until a review is given and then the child is back to where you were before, correctly doing all the problems.

Students with this type of problem need to be assessed to determine the level of their memory and recall issues.  Some students have these issues for the following reasons:

1.  They do not invest enough time into reviewing concepts and study habits are poor.  If they put in more time with proper and specific study habits, their memory issues could be reduced immensely.

2.  They have ADHD or ADD and can’t focus on something for long enough to keep the information in a fashion that allows for good recall.  When trying to recall the information, they are distracted and can’t retrieve the information due to their many distractions.

3.  They have a true memory learning disability that would require accommodations.

Let’s address #1 first.  We don’t just want to provide every student who can’t recall with accommodations to adjust for lack of recall.  First, we need to make sure they have tried all the necessary strategies for increasing their recall.  Most children have poor study habits.  Schools don’t teach students HOW to study, especially for math.  Most students feel the following approach for studying math is sufficient:

1.  Go to class – listen, maybe take notes

2.  Do homework – most of the time

3.  Night before test – do what ever homework teacher assigns, if teacher gives a review sheet then great, they get that review the night before, if not – there is no review.

4.  Maybe “browse” quickly through notes in notebook before test the night before.

For a struggling math student, the above approach is completely ineffective.  The following approach needs to be utilized and will have to be overseen by a parent – to help your child with a sufficient math learning disability, requires a large amount of work on the parent – if the parent does not do this, they really cannot rely on the child to do it themselves and the problems will persist.

1.  Parent:  check to see math homework gets done each night.

2.  Parent:  check to see how many problems were marked right and wrong each night from homework, if most are correct – no work is required, however, if student is getting less than 85% correct, parent needs to get tutor (or do on their own) to figure out what types of problems the student are getting wrong and start intervention on those problems immediately – n0t the night before the test.

3.  Parent:  have tutor (or self) check on concepts and vocab terms and make flash cards each night relating to vocab terms and HOW to do a problem or a concept relating to a problem.  For example, formulas might go on cards, definition of perpendicular lines, and things such as the steps for finding the Least Common Multiple if that is a topic that is covered.  Each night cards should be made.

4.  Parent:  Quiz student (and have student self quiz) cards daily (this is very important for memory!!!)

5.  Parent:  Review all quizzes that come through – quizzes are tools to see where your child is at.  If they get problems wrong on a quiz, they should make cards related to these problems and redo each problem and a tutor can create a similar problem with different numbers for the child to do.

6.  Parent:  Ask teachers for review sheets for tests – have your child work on a review sheet the night before the test, make sure you have an ANSWER key, there is no sense in having your child do the work if it is WRONG, you need to fix and problems they have THAT night before the test.  Teachers who assign review work without an answer key, makes no sense.  If you need to, hire a tutor to check their work and go over the problems they go wrong.

7.  Tutor:  A good tutor should find a series of Common Mistakes that your child consistently makes, make a note of what those are the night before the test and have the child review those mistakes so they are aware of the list so they don’t make those same mistakes on the test.

Remember:  You can’t have success if you wait until the night before the test to look for problems, especially with a child with memory struggles.  It won’t stick.  The child needs to have fixes in place and the correct material entering their brains in SMALL doses FREQUENTLY throughout a longer time period to be successful.  It is a lot of work – you can print out the list and hand it to a tutor and ask them to do the work if needed.  Tutoring should be geared toward your individual child, not group tutoring with one tutoring dividing time among multiple students.  Pay for someone with experience who knows what they are doing and remember just because someone can DO math, doesn’t mean they can TEACH math.  Craigs list is not the best place  to find qualified tutors.

Let’s say you have the ADD or ADHD student, you are in for more trouble with that kind of mind.  This kind of student needs smaller and more frequent work time.  Do not have math time be one long episode.  Make math into 3 separate sessions if possible per day.  Try all of the above as well with the ADD and ADHD student first.  If you find that these don’t work, look to our recommendations for the memory impaired child.

Let’s say you have really tried all the above suggestions and your child still cannot retain information even with all that hard work.  Your child may truly have a significant memory learning disability.  Please know that although there are “tests” that test for these things, they do not pick up all aspects of memory learning disabilities.  Most tests are for working memory and memory issues are more complex than this.  Working memory addresses holding information in your brain while working on a problem – since most students can do this fine, during regular sessions on the topic, they work the problems fine – it is just that they can’t retrieve this information from memory when it hasn’t been used for a certain period of time.  Therefore, don’t let school systems tell you that since a psychological test came back within normal limits, it means that the child doesn’t have a memory learning disability.

So what can be done for the child who really has a memory learning disability?  First, know that school systems are not likely to think outside the box.  Getting a school to do what is in the best interest of your child can be very difficult even though it makes perfect sense.  If you think about the goal of education, it is to get students to learn as much as they can.  If they have a disability, accommodations are put in place to allow them to learn despite that disability.  A blind student is given braille, a student who has a low IQ is given material that is lower than grade level, etc.  If the disability stops a student from moving forward, you need to ask what can I do to allow the student to continue to move forward?  It is not good to use words like, “what is fair for one student vs. another?”  I have had teachers and other students feel that if 2 students (one with no ability to memorize and one who can memorize fine) are given a test and the student with memory issues is given a formula while the other student is not, it isn’t “fair,” that student 1 gets the formula.  I ask, is it “fair” that student 1 has to solve a problem with no knowledge of a formula that is needed (because he CANNOT retrieve it from memory) while the other student has access to the formula because their brain works “normally” and can retrieve the formula after memorizing?  What is really fair?  Student 1 is sure to get the problem wrong since he does not have access to a formula.  That is not fair.  All we are doing is leveling the playing field for the student with the disability so that he or she can continue to learn and move forward.  Here are suggestions for the student:

1.  Students are provided  with formulas and definitions for testing

2.  Students are allowed a 3X5 index card with notes on procedural steps for performing math problems as needed for complex multi-step problems (especially in  Algebra)  Student still needs to be able to do the work and recognize the type of work needed.  Index card can be reviewed by teachers if needed to make sure reasonable information is provided.  Note, many college professors (myself included) allow college students a 3×5 note card on a math test to help with memory issues.  Teachers jobs are to make sure the problems are designed to test for conceptual understanding and procedural work is a by-product.  Remember that in the “real world,” people always have access to outside resources.

3.  Allow calculators for students as needed.  This can be controversial but I feel that the world is filled with technology.  Everyone always has a cell phone on them and therefore a calculator on hand.  The child may need a calculator to answer application problems so they can focus on the ability to problem solve (more important) than procedural steps involved  with arithmetic when calculators will always be available for college students and real world jobs.  Again, it is the teacher’s jobs to make sure their assessments look at students understanding of the underlying concepts and that can be done without just asking traditional procedural questions.  Teachers might allow notecards for the procedural work and calculators for the application questions.  This allows the teacher to see if the student really understands, for example, that a student knows that the problem involves multiplication even if the child cannot memorize their multiplication facts.

4.  Use right brain memory tricks.  Use songs to help students remember things or imagery.  This stores the information in another part of the brain that is often easier for students with memory issues to retrieve.

Good luck with your student.  I have my own child with memory problems.  He is a special needs child but with appropriate accommodations is capable of taking some regular education courses.  He took Algebra 1 and had two great teachers who supported the above accommodations that allowed him to be successful.  He was actually one of the strongest students in the class even though he cannot memorize!  His teachers even sometimes gave him 1:1 tests so they KNEW he totally understood all the concepts and it wasn’t in all cases that he needed his “memory” cards.  His teacher was great with songs that helped him memorize the quadratic formula.  In fact for the state test at the end of the year (which he did very well on), he wasn’t allowed all the classroom accommodations because of state rules, however, given the accommodations during the year, he learned enough and was strong enough that he did fine (the state provided some formulas anyway and the test was multiple choice so you can always solve in 2 ways) even without any notecards.  His success and accommodations should be a model for others with similar struggles.  He could never have passed the class without the accommodations and clearly left a very strong math student and a strong sense of math self-esteem after the experience.

Math self-esteem can be severely destroyed by bad experiences in school when you have a child who desperately needs accommodations and aren’t provided them so they continue to fail needlessly.  This has a lasting effect on students and makes future mathematics even harder.

My background:

North Carolina State University:  Mathematics Education, Ph.D. Minor – Statistics

Interests:  Curriculum Development, Special Education, Learning Disabilities, Psychology of Educatioin

Also:  MS – Mathematics with concentration Secondary Education; BS Mathematics, Minor:  Secondary Education, Philosophy

Experience:  Owner:  Learning Center 2007 – Present; College Professor (Undergraduate and Graduate); Certification HS mathematics

Working with students with disabilities for 20+ years

I provide Consultation Services for a fee, please contact via email:  Lynne@ALCeducation.com if interested

Services include:  Curriculum Planning, Skype Tutoring, Educational Planning, Special Education Assistance

 
 

Math Learning Disabilities

13 Jan

As an educator and owner of a learning center that specializes in helping children with struggles in academics, I see a variety of students with different needs in mathematics.  Many of the students say, “I am not good in math,” these sentiments are often echoed by their parents which reinforces to the child the idea that they are just one of those people that aren’t “good in math.”  What does it mean to be good in math?  What does it mean to have a learning disability in math?  I see students all the time that are reasonable math students.  They may declare they are not good in math because 1) they don’t really like math 2) it doesn’t come as naturally to them as other subjects 3) they are conditioned that is okay to think of themselves as “not good in math” 4) they have average or below average math teachers and 5) they think because they might need some help to get a good grade that is equal to “not being good in mathematics.”  However, most of these students are reasonably good math students, they might not be the exceptionally gifted math student who just gets things very quickly and easily but they are decent math students.  If I put them all in a class with a strong teacher and appropriate testing, as long as they were motivated to try, they would all do quite well.

It is rare that I see a child that I really feel has a true “learning disability” in mathematics.  Sometimes I will get a student who initially has poor math skills when they are young and they just need 1) time to mature into mathematical thinking and 2) good skills on how to approach problems.  However, once these two goals are met, these students will eventually fall into the category above.  I am working with a 4th grader right now who was sufficiently behind in 2nd grade but in the last two years has grown, shows strong number sense, and is building good problem solving skills.

It is the rare few, however, that do have an actual learning disability that concern me.  Children who by fourth grade that still show little to no number sense.  Here are some examples:  if you write 854-853 on a piece of paper horizontally, a 4th grader should have enough number sense to know that these numbers are just one apart and therefore the difference is one.  With a child who has a true math learning disability, even when you point out the patterns to them including that both start with 85, they still don’t know how to apply that pattern and information to finding a difference, in fact, the only way they can find the answer is to line up vertically and do the actual subtraction. These students will often have poor memory skills and you will teach them something but it will be forgotten a month later unless constantly reviewed.  They can’t learn mathematically vocabulary because it gets forgotten due to memory problems.  Although these students might be able to learn basic facts, they will still rely on elementary approaches to addition and subtraction.  While their peers will just get to the point that they will know that 7+3 is 10 or find a faster approach to 15-8 than counting down using their fingers, these students will still rely on finger counting for addition and subtraction.  They may have their multiplication and some division facts memorized if taught properly but will forget the steps of how to do multi-digit multiplication and division if not in the middle of a lesson teaching it.  They will lack the skills to solve most word problems and are unable to see how the mathematics we use relates to real world problems even in basic and simple cases.  Here is an example, tell them they start with a certain amount of money, go to the story to buy 2 things, the first costs $4 and the second costs $5, they leave the store with $3.  How much did they enter the store with?  These students will just start trying different operations, they will be unable, in many situations, to draw an appropriate picture and unable to reason out (even after given hints such as you will have MORE money going into the store than leaving the store) what operations to apply in the problem.  They will lack understanding of money relationships outside basic counting of coins and perhaps making change.  They may be able to do the most simplistic problems such as, ‘I have $10, buy a toy for $3, how much do I have left? ‘  by using key words or perhaps by understanding but as soon as the problem is taken to a higher level, the student loses all mental meaning of what is happening in the problem and how mathematics relates to the problem.

What can we do for these students?  First, it is important to really be able to distinguish the type of student mentioned here versus the late bloomer that needs more time to mature for mathematical thought and better problem solving skills presented one on one by a professional.  It is also important to not label someone as learning disabled in math just because they have poor grades in math.  Someone who truly understands mathematical testing, number sense, and is skilled and experienced should make the determination.  There can be many reasons for poor grades besides a math learning disability.  If it is decided that the student does have a true math learning disability, then a plan needs to be considered.  It should be a “moving plan,” so that as time progresses, adjustments are made based on the skill set of the child.  Initially, the plan might be more rigid but the child may begin to develop more number sense with later brain development and experiences and the plan can become less rigid.

The following skills should be fully assessed:

1.  Long term memory as it relates to mathematics.  Can the student remember vocabulary and/or mathematical steps and procedures after a period of time has passed where the child has not been presented that information?

2.  Short term and working memory.  Can the student learn and process information with a reasonable speed when being given new lessons that involve multiple steps that require short term and working memory?  Can the student pass tests being given that require recall of short term memory items?

3.  Can the student perform mathematical calculations with at least 85% accuracy without a calculator?  Addition, subtraction, multiplication, and division.  Do they have other disabilities (such as dysgraphia) that impact their ability to write appropriately or ADHD which allows them to pay attention to detail?

4.  Can the student understand mathematical word problems and solve problems related to the procedural steps they are learning?  Can the student make the connection between the mathematics needed and the situation in the problem?  Can the student draw a picture and explain in words, what the problem is giving as “given” information, what it is asking, and why the appropriate mathematics match the situation?

5.  Is the student limited to solving word problems only when they see key words rather than understanding problems that require a student to have both an age appropriate reading comprehension and enough number sense to link the mathematics to the real world?

6.  At what level can the child solve word problems?

a.  Only when they perfectly match problems word for word with new numbers of a problem just completed (copying strategy)?

b.  Only when they have key words that tell the reader what operation to do?  How many were LEFT?  (Left means subtraction.)

c.  Only when someone else reads them the problem? (But provides no additional help)

d.  Only when someone else reads them the problem AND breaks down the problem, explaining what is happening in the problem (I am talking about multi-step problems)?

e.  Only 1 step problems but in all situations – with no help and keys words sometimes not given?

6.  Can the student do procedural mathematics but lack conceptual mathematics?

The answers to these questions help decide what interventions and accommodations need to take place.  For some students, they will need to take a 3×5 note card with notes (sometimes written by a tutor if they can’t write it well enough) on what steps are needed to perform a mathematical procedure.  For example, the steps to solve a quadratic equation.

Some students might need to always have a calculator on hand even when their peers aren’t allowed one.  This allows them to move forward in areas that they can even if they lack the ability to get the basic memorization of facts complete or if they have dysgraphia or ADHD that causes constant careless mistakes.

Some students might need to have their own list of goals that are reachable by them but won’t be the same goals that the state has for their peers.  If a child is at one of the lower levels of problem solving, you need to lower your expectations and start requiring just part of the work.  Have the student just draw a picture of the situation to show they understand the story instead of solving it.  Give the student a one step problem instead of 2 step problems allowing more time for their brain to develop.

Let the parents know that their child’s goals are going to be different and although report card grades *may* (depends on school) be based on full grade level expectations, the teacher will give a separate grade based on these lower expectations that might be in reach of the child.  Gradually increase the expectations with the understanding that the rate might be very slow.  Don’t be afraid to give the student “crutches” when needed so he can still “walk” rather than just be stuck sitting in a chair.  If he has a calculator and an index card with notes, he may be able to learn a lot more than if you just give him a test without these “crutches,” and watch him fail.

 
 

North Carolina Common Core Math 1 – what is it?

11 Dec

As the owner of The Apex Learning Center, I see students from many different schools who come in for help with mathematics.  This is the first year that North Carolina has adopted the Common Core Standards.  North Carolina chose to implement these new standards without the funds to purchase any text books that support these new standards and have provided minimal to no teacher education relating to these changes.  From what I have heard, their idea of teacher education is a top down approach.  They meet with the lead teachers once or twice with information about the changes and those teachers are to pass the information on to the rest of the classroom teachers at the school.  The individual classroom teachers get no hands on training and the lead teachers get “information” but no hands on training.

I have mentioned this before but feel it is worth mentioning again that one of the big ideas of common core mathematics is the encourage conceptual understanding in mathematics.  Mathematics has three parts:  first, procedural knowledge – the ability to perform operations and get correct answers.  This can be done at levels such as addition and multiplication facts or even taking an integral using the chain rule and quotient rule combined in Calculus.  The level doesn’t matter, it still breaks math down into a series of steps that can be followed that end with a correct answer.  Procedural mathematics is very important, all of elementary school mathematics requires procedural mathematics for the majority of its work.  People who have basic procedural knowledge of mathematics can get by in the world but will often say, “I was never good in mathematics.”  They will not see the need for mathematics in everyday life because they don’t understand how it can be used in everyday life outside of the basics of procedural arithmetic.  The second part of mathematics is a conceptual understanding.  In this instance, students understand not just how to compute, but understand why they are doing mathematics.  They will have strong number sense; they can apply arithmetic to word problems including multi-step word problems.  They understand the idea that an integral measures the area under a curve or how mean, median, and mode can all measure the concept of what is “typical” about data but provide different answers in different situations.  The  third part is when students who are able to apply mathematics to novel situations. If a student is given a problem that uses the underlying concepts and procedures of mathematics they know but they have never seen a similar type of problem solved, this student can still solve the problem.  This last type of student has reached the highest level in mathematics.

If you look at mathematics history you will see that our educators who determine “what the world should know in mathematics,” have grappled with procedural vs. conceptual understanding.  A long time ago, we had a system in place and students were not performing at a level that was good enough in mathematics.   Math educators decided that it was because the focus was too much on procedural understanding and not enough on building conceptual understanding, hence NEW MATH began.  Ask people who went through the New Math period, they were lost and confused as teachers, who were not trained to teach New Math, tried to change their behavior and teach math more conceptually.  It was a disaster and scores reflected that, so after some time, they made a new movement that was called “Back to Basics.”  BTB followed New Math and was supposed to undo the years of confusion we put our children through by just going back to a more procedural focus such as getting math facts under their belts.  However, the BTB era did not achieve the desired results either so out of that came the NCTM Standards and No Child Left Behind.  Still, we find that we fall below in scores across the board, especially in mathematics.  A new group of educators got together and determined two things were needed:  one a common set of standards across the country and a focus on conceptual understanding (hmm… anyone thinking New Math here?)  Hence, we now have Common Core.

Back to  North Carolina, which is the only state I am qualified to talk about although I am told it is the same elsewhere.  Our department of education decides to adopt Common Core.  This post focuses only on Common Core Math 1.  This is replacing Algebra 1 for students.  All public students (public and charter school) who would have taken Algebra 1 this year are now in Common Core Math 1 instead.  I asked teachers, “What is Common Core Math 1?”  The answer I got was, “It is Algebra 1 with a few things removed and a few pieces of Geometry and Statistics added.”  This was the most common answer.  All our schools – this includes middle and high schools – are teaching CCM 1 with no text books and nothing more than some information passed down from their lead teacher or their own interpretation of what they read.  So what does this translate to?  How does this COMMON (which makes me laugh because the curriculum was much more COMMON when we all taught Algebra 1 than it is now) Core Math 1 look across different schools?  Is it Algebra 1?  Should students leave CCM1 with most of the skills from Algebra 1 intact?  Should they be able to solve absolute value inequalities, solve systems of equations, factor all types of trinomials, find zeros, do linear regression, write equations of lines from 2 points, and more? Or is it okay if students just do labs that let them play around with numbers in discovery learning and if they “discover” the concepts from these labs, great, if not – well… we presented a “conceptual approach” — wasn’t THAT what common core was supposed to be about?

Let’s take 2 different schools and compare what they are doing at the half way point of CCM 1.

School Number 1, we will call SN1 for short.  They are a charter middle school.  My son attends this school so I do homework with him every night in common core and therefore am very familiar with their choice of implementation of Common Core Math 1.  He was given an old Algebra book that they have used to teach the Algebra 1 that CCM1 is replacing at the beginning of the year to work out of.  I am told, they are focusing more on conceptual understanding and this text has a lot of word problems at the end of each chapter and those problems are always assigned.  Hmmm… is conceptual understanding the same as applications?  Not sure I equate those two things.  I am also told there will be some hand outs eventually to fill in concepts that are in CCM1 that are not in the book.  I haven’t seen anything yet but they are flying through the book so at the rate they are going – maybe there will be on time.  The book has 12 chapters.  The students will have finished 7 out of 12 at the halfway point.  The book contains topics that many Algebra books would skip and has a whole chapter on Statistics so it is very full of Algebraic topics, a few of which are even seen in a typical Algebra 2 course. Students have learned to solve multi-step equations, inequalities, absolute value equations and inequalities, they have solved y=mx+b problems with the typical questions (given a point and slope or given 2 points).  They had to learn all 3 forms point slope, slope intercept, and standard form (note that I did find somewhere in the CCM 1 standards that say Standard Form would no longer be taught, but that part of the standards was lost at this school.)  They had to explain equations from graphs and they are solving systems of equations using all 3 methods.  The teacher does not allow the calculator and does very little with technology.  Next semester they will learn exponents, factoring, solving quadratics, graphing quadratics, exponential equations, arithmetic with polynomials including Algebra 2 topics here of rational polynomial addition, and statistical concepts.  I am sure by now you can see this is simply :  Algebra 1.  To be honest, I am happy that my son is learning Algebra 1 because personally I think Common Core Mathematics is going to be a disaster and I want my son to know Algebra 1, Geometry, and Algebra 2.  I wish technology was brought into the classroom as that would allow for concept building instead of the procedural focus which is how it is taught if you ignore technology.

Let’s now consider School Number 2, SN2.  This is a public high school.  I tutor a freshman student who is taking CCM1 at SN2 three times per week so I am very familiar with her work for the class.  Remember there are no CCM1 text books so her school made packets for the course.  I have never seen anything more disorganized in my life.  I am still in awe that this is their idea of CCM1.  They don’t have any problems for students to work.  The student usually gets a very small amount of homework that is nothing you would see in an Algebra book.  So, they will not be leaving the course with experience doing any of the above mentioned things from SN1.  The teachers are trying to build conceptual understanding with no procedural requirements to the class at all.  Their book is a series of lab experiments that the students are supposed to infer mathematics from.  It never directly teaches anything.  The homework never reinforces anything and is very arbitrary.  Many nights there is no homework or maybe 2 questions.  My student is getting a poor grade because it is very difficult to tutor someone when you are not inside the “brain” of the creater of this curriculum since it is so chaotic and there is no practice for the students. You don’t know what the teacher wants them to know.  The students don’t get to bring home tests, so I don’t even know what they are asked although at one point there was a question about finding slope (a procedural topic) on a test and the students pointed out to their teacher that he never taught them that.  He realized it and gave them a quick lesson and then let them retake those test questions.  He didn’t link that to anything.  I am thankful that in my student’s 8th grade curriculum, before the switch, (I tutored her then also) she had enough Algebra that she knows how to find equations of lines and other basic Algebra skills that she isn’t losing an entire semester/year.  However, next year the current 8th graders who are in CCM 8th grade won’t be so lucky since those Algebra skills have been removed and “supposedly” placed in CCM1 although at this school, they are not there.  To date, the students in SN2 have had a unit on Statistics, they can solve multi-step (but not too hard) equations, and they haven’t worked with inequalities much except to say “at least means” greater than or equal to and basic ideas such as this.  They have been studying functions in a round about way for a long time – they can name domain and range and tell if something is a function or not and find f(4) if f(x) = x + 3.  They can calculate slope and they learned NOW, NEXT commands for associating one variable with another.  This approach has done nothing  but totally confuse my student, she doesn’t see any links or connections and has no idea at all about what they are even working on.

The course material for the same course at SN2 vs. SN1 is so totally different.  Neither of them are following the spirit of the Common Core Standards.  As is usually done, things are at one end of the extreme or the other.  SN1 is teaching a typical procedural Algebra 1 class with applications.  They are not using technology and not building conceptual understanding within the context of the course.  They are not following the standard guidelines by removing things that are outdated such as switching forms in Algebra to standard form and are covering topics that are reserved for other courses when the time could be spent exploring with technology.  SN2 has gone to the other extreme, they have done away with all procedural methods and are trying to get students to understand mathematical concepts through labs and explorations with very little practice from the students, without good structure, and they are very behind.  Students in SN2 will leave CCM1 with an incredibly weak understanding of mathematics and will be far worse off than they were taking Algebra 1 at that same school last year.  Part of the problem is the curriculum and part of it is the lack of teacher training given to the teachers to implement this curriculum.  However, the biggest part at SN2 is whoever made these packets missed the boat on what the objectives of CCM1 is supposed to be and how to impart this knowledge to 14-16 year old students.

For comparison sake, I looked around at other CCM1 NC blackboard sites to see what other schools were doing without any state guidance for CCM1.  The results were very varied.  Many were like SN1 and just a repeat of Algebra 1.   Other schools seemed to be trying to do a hybrid of traditional Algebra 1 but put a great emphasis on certain topics such as exponential functions.  I did not find another school with a curriculum anything like SN2 but that doesn’t mean it isn’t out there.

In conclusion, is CCM1 just New Math all over again?  Are teachers equipped to handle teaching CCM1 at the level designed by Ph.D. educators without the years of instruction that the creaters had when coming up with the concept?  Is Common Core at all Common?  I have clearly found the answer is no and by the way this extends into the elementary school as well.  If it isn’t even Common within one state, how is it Common among all states adopting Common Core?  I would love to hear from you!

 
 

Grades, what do they really mean?

02 Nov

I run a tutoring center and tutor students in Wake county, North Carolina.  I get students from many different schools, although they are all in the same county.  However, their courses, although identical in name and in “theory” content, vary greatly.  If the level of a course can range from easy to extremely difficult and yet we award a grade based on test scores to both classes, how is this fair to the student and how is this truly a measure of anything?  Here is an example.  I am currently working with a student taking Honors Geometry through Wake County Virtual Public Schools.  This is an online class given when the school is not able to provide instruction within the school.  In this case, the student is in a middle school that does not offer this course so he has to take this online version of the course.  There is only a virtual teacher who responds to questions that the students (currently 3) ask and it takes about 10-20 minutes before they get a response to each of their questions.  There are no in person lessons, just self teaching from online materials.  The students turn in assignments and their assessments are never looked at by a person, they are always multiple choice so that a computer can grade all their work.  In a typical “in house” Honors Geometry class, students are expected to do 2 column proofs on exams, however, since this is not possible in an online class (it can’t be graded by a computer) these types of problems aren’t given.  Proof type questions might be asked but in a multiple choice format, which is hardly the same as generating a proof from scratch.  The students still have to do some exercises with proofs but aren’t tested on these proofs and their exercises, I am told, count about 10%.  It seems the multiple choice questions are quite easy and a student who in a “in house” Honors Geometry class who might not be passing with the same level of knowledge, can score a B in this multiple choice testing format.

On the other hand, I also see a huge variation from one school to another.  For example, School A’s Honors Geometry program is so challenging that even I can get stumped on some of their questions from time to time and I have a Ph.D. in Mathematics Education, Masters in Mathematics, etc.  The level of proofs required in School A are truly much harder than I feel is appropriate, especially considering it isn’t in line with other schools and way off from the virtual school.  I tutored a student from School A who is extremely bright, knew so much about Geometry that most high school math teachers (outside of School A) who might sit down and work with this student would be very impressed with this student’s knowledge of Geometry but since he attended School A, his grade for the year was a C!  If he had been in School B, he would have gotten an A, if he had taken it online, he could have slept through the course!  School B is right now the road from School A but the same math classes – and I am not just talking about Honors Geometry but all other high school math classes  – are so much easier at School B than School A.  School B requires a much more reasonable amount of homework as well.  School A requires way too much from kids and somehow thinks that if they assign 60 problems of the same type that will make the kids smarter.  My son is 11 now and smart enough to take Honors Geometry but if he has to take it at School A, I won’t let him.  In fact, I am not sure I will sign him up for any honors math classes at School A because their math program is so out of line with what is reasonable – and if you happen to get a less than stellar teacher in the mix, then just forget it!

These grades students make determine many things for students in high school – they make up their GPA – this makes them competitive to get into colleges.  How does that C in Honors Geometry look to a school like Stanford?  They perceive the student as a poor student, when in fact, this student had he been down the road in School B, would have straight A’s in Honors and AP math classes!  What a difference in perception and yet it is the same student, the same knowledge.  All School A did was make the student get frustrated and feel like he can’t be successful in math and now this student will choose not to continue on with Honors and AP math classes that he is capable of.   I have to tell the student that it ISN’T him – I hate to put blame on outside forces with teens because it is important for teens to learn to take responsibility for their actions, however – when I work with a very bright student and watch him achieve a C (and it wasn’t for not doing assignments, etc.) – there is nothing else I can do but try and help salvage the student’s math self-esteem that School A has taken away from him.

Another example; a parent calls me – her son is failing – well almost, he barely has a D, in Algebra 2.  He is generally a B student in math.  She begins to relay the story.  The teacher, who gives math credit for whether a student uses the bathroom during class, is telling her that her son has only completed 47% of his homework.  Well, one would argue, if a student isn’t completing their homework, that is a reason for a poor grade.  However, despite the fact that she said those exact words, the truth is that he did 100% of his homework but she graded his homework and he only got 47% of his homework correct so he has a 47 homework GRADE, not that he only did 47% of his homework.  However, isn’t homework supposed to be for learning, not an assessment?  Why are we teaching a new topic, assigning homework, then grading it the NEXT day, and weighing it so heavily that it takes a student that has a B average on tests and lowers his grade to a D (almost an F) in the class?  Shouldn’t you be able to come to class the next day and say, “Ms. Teacher, I didn’t understand homework problems # and #, please go over these.”  This is how it always worked for me.  This is how I always taught.  This teacher scores the homework and weighs it so much it fails him even though his understanding on true assessments is a B.  Now when colleges see his transcript, yet again -they think this child is a D student when his knowledge of Algebra 2 clearly indicates a B level of understanding?

What are these GRADES supposed to measure?  Whether we use the bathroom?  If we could do homework the first night it was assigned?  If we can do super hard proofs when other students can get A’s in the same class for basic multiple choice questions?  How is this an accurate measure of anything?  And yet, it has an impact on what college a child gets into, if they get scholarships for college?  I remember one college professor I had, he got it right.  He gave us tests, we took them and got grades (this was in math).  Our final exam was cummulative – it tested everything for the whole class.  If we knew everything on the final, then we had proven we had mastered everything we were supposed to learn in class.  So, he said to us – IF you take the final and your final exam grade is higher than your grade would be if I factor it in at 20% (or whatever the assigned weight was), I will just give you the grade you scored on the final.  So, if our grade going into the final was a D but we got an A on the final, we got an A in the class.  Why?  It made sense … What is the purpose of a grade?  To measure your knowledge of the class content?  He didn’t care WHEN you managed to “get it” – if it took you longer but you got there by the end and could demonstrate it on the final – you proved you mastered the material in the class so your grade should REFLECT your ACTUAL knowledge at the end of the course.  It was BRILLIANT!  Dr. Kenton, you are a brilliant man and teacher!

Speaking of grades – tell me if this makes sense – Wake County schools offer higher quality points towards the weighted GPA based on Honors and AP classes.  If you take a regular class and get an A, you get 4 QP, if you take an Honors Class, you get 5 QP, but if you take an AP class, you get 6 QP.  So, why do you get 6 QP for an AP class?  Well, it makes sense because AP classes are supposed to be college level classes offered in the high school.  So, college level work should be awarded more QP than an Honors level high school class, right?  That makes sense.  However, if the student actually goes TO a college and takes a college course AT a college, the county’s policy is to award only 5 QP for an A.  So they equate an ACTUAL college class the same as an Honors level high school class – giving more weight to an AP class than an actual college class taken in college.  So I could take AP Calculus BC, get an A and get 6 QP but if I take Calculus III as a dual enrolled student the following semester while still in high school and get an A, the school will only give me 5 QP for it.  So it would LOWER my GPA and make me LESS competitive for colleges looking at my GPA and class rank.  Again, pointing out these grades are meaningless.

My final comparison is the grading scale used.  Most schools use a 10 point scale.  90-100 A, 80-89 B, and so on.  So if you are in states with this scale, and you get an 84, you would have a nice solid B.  However, Wake County decided that they wanted to make things more challenging for their students and now use a 7 point scale, so that same 84% would equate to C in Wake County schools.  Do colleges take this grading scale into consideration when looking at applicants?  These inconsistencies make the meaning behind grades useless.  When I taught college and graded, I preferred to think of grades this way – to me, an A meant Excellent Understanding, a B was Good Understanding, a C was Fair Understanding, a D was Poor Understanding, and an F was Little to No understanding.  After I computed a numerical grade for a student, I was looked at the student and said if I didn’t have any true grades and just looked at their “understanding” and had to attach a word to their understanding – how would I define it – excellent, good, fair, poor, or little to no – I wanted to make sure their numerical score matched their TRUE understanding – luckily, it did because I was very careful with each individual assessment but this was especially helpful when students were borderline and I had to choose between two letter grades.

I chose to homeschool my son for one year of high school.  It was so liberating to not worry about grades and just have him learn for the sake of learning!  Of course, we had to “make up grades” for his transcript to send off to college.  I tried to think about what he would have gotten if had taken the class in a public school.  He always got B’s in English in traditional classes, so I gave him a B in English.  Things he was passionate about and worked hard on because he just really wanted to learn and master (which he did) – those were clearly A’s.  None of that really mattered to me though, he learned what he needed to and worked really hard at what was important to him.

In closing, I think back to my undergraduate years when I was minoring in Philosophy and one thing that interested me was the concept of a grade-less school.  In the book, Zen and the Art of Motorcycle Maintenance, the author wrote about a professor he had who chose not to grade his college class and instead let the students choose their grades.  It was a great read and I would encourage everyone to check it out.    I would welcome any comments on this topics.

 
 

Scope & Sequence in American Mathematics

18 Sep

We do it all wrong!

Why?

1. To give students a wide breadth of mathematical knowledge
2. Because our teachers don’t know how to teach math very well
3. Because we don’t have our act together and repeat, repeat, and repeat
4. Because we feel the need to give TONS of the same type of problem
5. Because our students don’t GET MATH and we think that means we need more problems and more repetition

If we learn how to teach math better and don’t waste time with so many worksheets of the same problem and don’t confuse students with so many different mathematical topics, we could progress at a faster rate with knowledge retained by students.

The NCSCOS (North Carolina Standard Course of Study) has goals in 1) Arithmetic, 2) Geometry, 3) Statistics and Probability, and 4) Algebra and 5) Measurement. One day our teachers will be teaching factor trees, then the next they are switching to Geometry vocabulary (what are acute angles? What does it mean to be perpendicular?), the next day they are having the students do “pretend” Algebra, where we don’t actually do what would be done in Algebra, we hide it, with a missing addend instead of a variable, and then students are doing graphing and finding out how many combinations exist if I line up 4 books on a shelf, then they are working with the metric system and measure items using how many “book lengths.”

This breadth of knowledge is good but I fear that we lose so much by constantly shifting gears on our kids. They forget what they learned in the Geometry unit in grade 4 when they get to Grade 5 and we start all over again. The “Algebra” skills are not really helpful yet until the kids can grasp more advanced ideas and the uses of Algebra. Measurement, to some extent, is necessary – certainly telling time, using a basic ruler, and money. Probability and Statistics are very useful, but again, let’s finish one thing before we address a new thing.

Here is what I see as a draft of scope and sequence for elementary and middle school mathematics:

Grade K:
1. Skip counting – by 2’s, 3’s, 5’s, 10’s. Expanded skip counting by 5’s and 10’s. What if I start with 25 and now want to skip count by 10? Apply to learning to count money.
2. Tally counting and apply to telling time.
3. Adding – group by ability – some can add all 1 digit numbers here, some will need to just add low numbers +0, +1, +2.
4. Exchanging – Using base 10 blocks, teach the idea that for every 10 units you can trade in for a 10 block.
5. Modeling place value with 10’s blocks for units, 10’s, and 100’s.
6. Reading numbers to the 100’s.
7. Learning doubles: work on memorizing (using song is helpful) all the doubles.
8. Adding to 10 (10 + 3 = 13) Build the concept of place value.

Grade 1:
1. Mastery of counting money
2. Mastery of telling time
3. Adding numbers without regrouping
4. Using what was taught about regrouping in Kindergarten, expand to modeling addition with regrouping
5. Add place value to the 1000.
6. Teach addition strategies.
7. Introduce the concept of multiplication and how it applies to addition and begin study of multiplication
8. Begin unit on subtraction and teach subtraction strategies
9. Teach basic measurement

Grade 2
1. Review units on telling time, counting money, addition of numbers with and without regrouping, subtraction
2. Teach multiplication strategies
3. Teach concept of factors
4. Link multiplication to division
5. Begin the process of modeling with division
6. Do mixed word problems, teach wording of problems involving +, – , X
7. Expand place value
8. Introduce concept of fractions & decimals
9. Order decimal numbers
10. Do 2 digit by 1 digit multiplication

Grade 3
1. Solidify multiplication
2. Build to long division
3. Equivalent fractions
4. Adding fractions with like denominators
5. Using equivalent fractions, add with unlike denominators
6. Multiply fractions
7. Divide fractions
8. Introduce decimals and how they relate to fractions
8. Introduce concept of percent and how it relates to fractions and decimals
9. Convert between percents and decimals
10. Add and subtract with decimals
11. Discuss degrees (90, 180, 270, 360) – do turns with your body

Grade 4:
1. Introduce mixed numbers
2. Add & subtract with mixed numbers – use models
3. Convert mixed numbers to improper fractions
4. Multiply and divide with mixed numbers
5. Apply real world uses of percents (interest)
6. Discuss concept of variable
7. Use variable to represent unknown in math problems
8. Introduce Perimeter and Area and practice arithmetic by applying these two problems

Grade 5:
1. Discuss multiples and factors
2. Build factor trees
3. Find GCF and LCM (relate LCM to equivalent fractions)
4. Probabability and Statistics UNIT
5. Begin Pre-Algebra

Grade 6:
1. Algebra 1 with modifications (1/2 year)
2. Geometry Unit (1/2 year)

Grade 7:
1. Finish Algebra 1 curriculum (1/2 year)
2. Probability and Statistics UNIT (1/2 year)

Grade 8:
1. Advanced Algebra 1 (for students who are struggling – this is a full Algebra 1 class with topics from Algebra 2 introduced at a basic level) OR
2. GEOMETRY

Grade 9 – all students will be ready for Algebra 2 or Geometry

 
 

All About Spelling

13 Jun

All About Spelling Program

Link:  All About Spelling Page

Schools have gotten lazy about teaching spelling these days.  Many of the spelling programs start off teaching some basic phonics but reach a point where they just “assign” spelling words and expect children to memorize the spelling, do some worksheets, and pass their spelling tests each week.  Lots of children cannot learn this way and as they get behind in spelling, the teachers just push them further ahead as a group instead of back-tracking and really “TEACHING” children how to spell.

When we began to have these troubles with our 8 year old son, we realized he was failing his spelling tests in the third grade and couldn’t spell words he should have gotten in the second grade.  He had no strategies being taught and was just expected to memorize the words.  As an educator myself, I researched to find the best spelling program available that would use a multi-sensory approach, teach rules and strategies, and build a foundation in spelling.  I found this in the All-About-Spelling Curriculum.

The first day I read through the program, I realized there were things I didn’t even know about spelling.  When in school, I was taught that the “magic or silent” E would make a vowel say it’s name as in the word “time.”  AAS teaches other uses of the “magic E” – for instance, it is used to make the g say it’s soft sound in a word like “large,” it also stops a word from ending in a u or a v, like “twelve.”  Did you know that English words do not ever end in a v or u?  Lots of these concepts are taught in a comprehensive, multi-sensory approach to spelling.

Please click on the affiliate link above as we will get funs to continue to support the time needed to find and research the best curriculum programs if you use our link and choose to purchase the program.

 
 

Chinese Character Test

13 Jun

我爱我的妈妈。

这是我的爸爸。

我有三哥哥。

我有两小猫。

我有一大句。

我的大句像吃鸡肉。

小猫也像吃鸡肉。

I am teaching my six year old daughter Chinese and wanted to test to see if the words we are working on will show up well on a blog post.

**Worked good on my computer!  Although it might now work on computers that don’t have the Chinese Characters Enabled.