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Posts Tagged ‘Stop Common Core NC’

The Good and Bad of Common Core Mathematics

21 Dec

Initially I was opposed to Common Core Mathematics and in general, I would say that I am still anti-common core but not for the same reasons that many others are anti-common core.  Since I was against CC, I joined some Stop Common Core groups and visited some groups who support doing away with Common Core.  I listened to a very interesting debate with a Pro Common Core Side and Stop Common Core side and was very disappointed in the ability of the side that was against Common Core to debate its argument effectively.  I also became very disappointed with the arguments of many of the people who were anti-common core.  I don’t believe the larger political argument that it is Bill Gates trying to take over the world and any generalized arguments on that point.  To be honest, I would support a common core if it was good and effective. My feelings of anti-common core (and I am mostly speaking in the area of mathematics because that is the area I am qualified to address) are solely with respect to the effectiveness and appropriateness of the curriculum and its ability to improve mathematics in the classroom.

As a mathematics educator, someone who has a Ph.D. in mathematics education, and someone who actually works with kids at all grades and all levels of ability, I applaud and understand the INTENT behind the goals of the mathematics common core.  When you look at the goals, the expectations, the curriculum, and what the educators who wrote it had in mind, I can clearly see what they WANTED to achieve and on many levels it is wonderful.  The problem that they failed to see is that the implementation of these goals was not feasible and has created utter chaos.  Let’s take an example.

In elementary school, one “common core” objective is working with the decomposition of numbers.  This means the ability to break numbers apart into pieces to create more friendly numbers to make math easier to work with, often in your head and sometimes on paper.  For example, if you were adding 213 + 23 in your head, a mathematician might first add 210 plus 20 to get 230 and then add the 3 afterwards to get 233.  Mathematicians (read Ph.D.’s in math education here too) have a natural number sense to regroup numbers that allow you to add and subtract more efficiently in your head.

So… our wonderful creators of Common Core, thought, “well if this is what good mathematicians do automatically, this is what we should TEACH all kids to do.”  First it will allow them to build more number sense since they will have to understand how numbers are broken up and go back together (place value, etc) and second they will learn how to do math more efficiently.  All of this is good intent, it makes sense on a pedagogical level.

HOWEVER – what did this TRANSLATE to into the hands of TEACHERS and CURRICULUM WRITERS and in the eyes of PARENTS (and filtered down to CHILDREN)…

First, some children will just naturally decompose numbers – the kids that math comes easy to anyway, will just do it on their own!  The kids that math does not come to easily, do not tend to decompose numbers on their own for a reason, it is hard for them, they don’t build number sense at the same rate as the child who would naturally decompose numbers – so the age at which our CC creators choose for us to have kids LEARN to decompose numbers may not be DEVELOPMENTALLY APPROPRIATE for all children. This is a common problem with lots of Common Core Mathematics.

Second, elementary teachers are teaching children to decompose numbers – this is not something they were taught to do, elementary teachers get VERY LITTLE training in how to teach math and even less time in how to teach math this NEW way, the common core way, which is certainly not how THEY learned math.  So, the lessons may be confusing for students and the reasoning behind WHY they are decomposing numbers may be lost because these elementary teachers are not the ones with Ph.D.’s in mathematics education who understand the theory and the why’s behind all of this.

Third, the reason for decomposing numbers is usually to provide the ability to do math quickly in one’s head, not to do it long hand on paper – but again this got lost in translation, the teachers and curriculum writers don’t understand the REASON behind the goal, they just know the goal:  Decompose numbers and learn to add this way (because this is what the higher ups say is good to do).  So, now kids are learning to add numbers on paper using friendly numbers where it takes 5 minutes to do a problem that should take 1 minute if using the most effective way.  By this I mean, if it is small enough to do in your head, you should use the friendly number approach and decompose your numbers BUT if they are big numbers, you should use the traditional algorithm and do it on paper.  Students should be learning to take the most efficient approach and that the reason for decomposition and friendly numbers is that it will help them with mental math but there is still a place for the traditional algorithm and this method is not meant to replace it.

It got to the point where parents would post “bad” math common core homework assignments on this Stop Common Core site so everyone could see and comment.  At first, there were legit bad assignments –

  • some were developmentally inappropriate
  • some were new common core ideas that had no directions so both parent and child were lost or used vocabulary that the teacher had never provided to student / parent
  • some were things that I just mentioned, where it was something that was completely out of context, long tedious multi-step problems that could and should be done more effectively with a traditional algorithm

but, it reached a point that parents began to just be ANTI-COMMON CORE and ANY and ALL math homework was bad in their mind and they were posting things that were:

  • assignments that you have seen pre-common core
  • very good assignments that taught strong math concepts
  • anything that was slightly different or didn’t require the memorization of math facts was considered BAD

So, I want to make a point that being anti-common core doesn’t mean you agree that all of common core is bad.  I see a lot of merit is the ideas behind common core math, however, the implementation is a disaster and I feel strongly until (and if) that can be fixed, we are simply confusing students more.  Teachers are requiring students to “only do it the common core way,” instead of saying, “here is a tool box,” use this tool box but as long as you get there – both procedurally and conceptually, I don’t care how you do it.  I also think that Common Core pushes the concept and the why too much at the expense of the procedure.  Again, to do math, you need to have a tool box of procedures, the why and the applications come for students who are successful with strong procedural knowledge and when we over-focus on the concepts and the essay writing, students lose the practice time which also helps the light bulbs go off.  There has to be a balance.

 

Lynne Gregorio, Ph.D. Mathematics Education

 
 

Learning Mathematics Through Achievement Learning Based Model

07 Apr

What is an Achievement Learning Based Model in Mathematics?  This is a developmental model where the student has mastery of one topic before moving onto the next topic.  In using this model, one would first need to identify your academic goals.  For most educational institutions, the academic goals is that the student learn and maintain that learning.  Currently, most school systems use a model of a set of curriculum standards, currently the Common Core standards in much of the United States for Mathematics, and students are exposed to a classroom with objectives to teach these concepts that lead to the understanding and mastery of the standards.  Students start in Kindergarten and each school year is generally broken into 4 quarters where teachers are given a pacing guide so that they can get through all the objectives needed to FINISH the standards for each grade level.  Students are given classroom assessments along the way, including possibly quarterly benchmark tests and in later grades some type of End of Year test that measures the mastery of the standards for students.

The teachers are generally not allowed much freedom in deviating from this pacing guide and required topics that they must get through since these are all prerequisites for the knowledge base students will build on during the following year.  In the early elementary years, United States students actually do fairly well overall keeping up with the pace, although, there has been much controversy over the Common Core Standards for many different reasons including political reasons, lack of testing, and pedagogical methodology.  At some point, however, students (probably almost all students at one time or another) will come across a concept, unit, or topic either in elementary school, middle school, or high school where they will get confused.  There is no time built in for teachers to realize that the class is “lost” and they need to spend longer on a specific topic.  There isn’t even the flexibility for teachers to “speed up” when topics are easy so that they can slow down later when needed.  I have seen teachers finish a unit early and just give students “free time” since they were off their pacing guide.  Teachers are not being taught about “reading” students for understanding and “how to adjust” their lessons based on individual class feedback when taking methods classes because this isn’t even allowed anymore.  Teaching is no longer an art that allows for creativity and talent and therefore all the good teachers are leaving the profession in droves.

Let’s pretend for a minute that we care about student learning as our main goal.  If we consider an Achievement Learning Based Model, we can put student achievement before our need for control, before our need for cattle car education, before our need for convenience.  An Achievement Learning Model would require more work but in the age of technology, it is so very doable.  Many schools are considering a flipped curriculum these days.  A flipped curriculum if done correctly works like this:  lessons for each unit are taped, students watch the tapes for homework and then when they come to class, they spend classtime doing active learning with a teacher available for help.  Note, this is not time when the teacher sits and grades papers or takes time off, the teacher is actively participating with the students but it allows them time to have someone help with the active learning part, working problems rather than the static part of learning, watching the lesson.

Here is how the Achievement Learning Model can be added into the flipped curriculum model.  Let’s say that you have a group of high school freshmen who are taking Common Core Math 1 or Algebra 1 (we will just refer to to it as CCM1 here.)  Students will get a goal sheet of the units they need to cover, homework needed to turn in, and assessments they need to complete.  Students will watch the lesson at home.  The next day they come into the classroom and they work on problems assigned to them.  They start with easy problems and get problems that get more difficult as they are successful.  Once they are getting enough problems correct, they move onto to the second unit.  For some students this might be one day, for other students it might take longer.  When it gets close to quiz time, the student takes a practice quiz and self corrects the quiz.  The goal is that they don’t take an assessment until they are having success with their homework and practice quizzes.  If they did well (show mastery), they take their quiz, if not, they work more problems, get more help.  Each student works at his or her own pace.  However, the teacher does oversee the pace of each student and certain requirements are placed on students who are not putting in the effort (which is different from those struggling with the content).  At school, there are after school hours in place for students to come in and continue the same “work” they would do in class.  Every student will be successful since they don’t move on until they have shown success.  The goal is 4 years of math so students “take” math every semester, where a student ends up in their knowledge base will be different for every student.   At the end of CCM1, some will have finished the course and be ready to take the final exam.  If any finish early, they will be helpers to the remaining students!  What a great way to reinforce their knowledge.  If a student does not finish, they can continue in CCM1 the next year until it is complete and move into the CCM2 whenever they finish and start there.

Bright students may have a schedule that looks like this:

Block scheduling:  (just a sample)

First Semester        Second Semester

CCM 1                            CCM2

CCM3                             Precalculus

Calc AB                         Calc BC

AP Stat                          CCM – helper

 

 

A slower student might look like this:

First Semester           Second Semester

CCM1                               CCM1

CCM1                               CCM2

CCM2                               CCM2

CCM2                               CCM3

CCM3                               CCM3

 

Each student takes math every semester, each student has mastery but they get to do things at the pace they need and they will know far more mathematics than our current model where many get D’s and forget what they have learned.   This model needs the following to be successful:

1.  A good teacher who is excellent at explaining the content on the videos is easy to follow steps and includes problems for the students to “practice” while watching the video that shows that the student watched and paid attention to the video.

2.  A good curriculum writer who can create good practice problems so that students can have sufficient practice until they reach mastery with problems starting easy and getting more difficult and have practice quizzes and tests for students to take so that they know when they are ready for the real exam and ready to move forward.

3.  Teacher education where teachers are taught how to manage this new type of classroom, facilitate appropriate groupings among students working on the same topics, “read” students so they know who knows what and who is confused, be able to delegate helper students from within the class to students who need help, to be able to provide the best use of their time during the regular “workshop” settings of daily education.

4.  Test to see at what age students would be mature enough to handle “self” learning, although it will be new and a great skill that students will be learning so it is expected that students will have a normal adjustment period despite maturity issues.

 

Written by:

 

Lynne Gregorio, Ph.D.

 
 

The problems with Common Core Math 2 – why students are failing

18 Jan

As I watched one of the students I tutor fail Common Core Math 2 for the semester, I can’t help but ask myself, what did I do wrong?  Another student, passed the class (with an A, I believe) but failed the exam (the teacher chose not to count the exam towards the course grade).  Any quality teacher who has students “fail,” should ALWAYS ask themselves, “What changes do I need to make?”

So, I pondered this question.  I looked at the type of student that each student was, the type of teacher each student had, the school each student attended, and the work we did together in our tutoring sessions.  I was able to find my answer after these considerations.

The first piece of the puzzle comes from the type of student I worked with.  One student was a student who spent many hours studying and lots of extra effort above and beyond our tutoring sessions.  I also like to rank each student with how “easy” math comes to them.  On a scale from 1 to 10, with a 1 representing a student who really struggles to grasp mathematical concepts, struggles with number sense, and just doesn’t have a logic / math brain to a 10 where the student just “gets” math without even trying, math just makes sense automatically and is like breathing, I will rank each student to provide prospective.  This student is probably around a  7.  The other student did not spend any time outside of our tutoring sessions working on math, didn’t really see doing well in math as a priority and ranks lower around a 5.  She doesn’t get totally lost but can’t seem to put the ideas together and connect them.  She also doesn’t spend time memorizing what is needed to do well.

The second piece of the puzzle comes from the school system, school and teachers these students have.  Both students are in the same school system but at different schools.  One school clearly has higher expectations than the other school and tends to ask harder questions on tests.  Neither teacher seemed “terrible” or “good.”  Neither teacher seemed to care too much about the success of their students based on my interactions / discussions with their families.

These previous two pieces certainly play a role in student success.  From me, both students got the same help from me but students need to spend outside time studying, memorizing, and practicing problems to be successful.  However, one of the biggest challenges I see is that the pace of the curriculum, especially since this school system uses block scheduling (math classes are 90 minutes a day and an entire math class is completed in 1/2 year).  If you have a student who ranks a 7 or above, they can probably handle the pace of learning Common Core 2 in one semester but for students who struggle with math (especially for those with weak math backgrounds, poor number sense, poor study habits, etc.) expecting them to be able to pass Common Core Math 2 in one semester is akin to expecting someone to become an expert on Calculus in 10 days of lessons.  There is only so fast someone can learn information and that is not being taken into consideration.  Why aren’t we offering a Common Core Math 2A and 2B class for students who need to learn at a slower pace?  They did this for Common Core Math 1 (in fact that is your only option in our county) but for Common Core Math 2, your only option is to learn the entire content in 1 semester.  For bright / math minded students, it is a good option and should remain so that these students can move ahead and take AP Calculus and AP Statistics during high school but for the average or below average student (in mathematics), we need to offer math at a slower pace.

Currently, we pass students on with a D in Common Core 1 into this fast paced Common Core 2 class.  Students with a D in Common Core 1, are not prepared to even take the content of Common Core math 2, let alone take it at the pace of 1 semester.  Many of these D students were “gifted” their D’s as I have witnessed.  I have students who can’t solve a basic linear equation on their own, couldn’t tell you the difference between linear, quadratic, and exponential equations, and couldn’t solve or graph any quadratics receive a D in the course and now I know they will be completely lost and unsuccessful in Common Core 2 because they do not have any of the prerequisite knowledge needed for success in Common Core 2.  Yet, teachers continue to “pass” students along because they can’t “fail” too many students or they will get in trouble with the administration.

We seem to forget what the goal is.  Do we want to just pass students along or do we want them to have an understanding of mathematics that makes them college ready?  If we need to slow things down, allow students more time, allow students to repeat classes, then this is what we should do.  We also continue to allow lateral entry teachers because we are short on math teachers, yet we don’t value them.  Lateral entry teachers (and many current teachers) seem to lack the skills needed to help students learn how to study mathematics, another important step for success.  Rarely do I see students come to me with a list of topics they will be covering, review sheets with problems and solutions that are representative of what they will be tested on for quizzes, tests, and finals.  If students had these materials, they could learn more effective ways to prepare for mathematics assessments and be more successful instead most of my students have no idea what to expect on their assessments and no problems that are representative of what they are supposed to know and practice right before an exam.

 
 

Alternative Ways to Teach Mathematics for Common Core – in response to video for TERC

03 Aug

What do you think about this?  This came from a site called Stopcommoncorenc.org

 

Note this link comes from a site that clearly has a negative opinion about these alternative methods.  Is she justified?  Well, let’s not jump to conclusions and say, “Yes.”  I think the answer is “almost yes.”  I am a firm believer that nothing is ever black and white.  Common Core mathematics encourages students to learn alternative ways of thinking about mathematics.  They encourage students to delve deeper into the meaning behind the computation.  They want students to know the meaning behind an algorithm at a mature level.  This is a very LOFTY goal.  In fact, after doing my dissertation, I learned that many teachers don’t even have this level of understanding.  My daughter was taking 5th grade mathematics this past year using the North Carolina Common Core curriculum.  She was required to solve all her problems three different ways and then she had to write a journal entry that explained the WHY behind what she did.  This really isn’t too far off from what is in these videos.  Of course she was also taught or allowed to use the standard algorithm, but only in addition to other less effective algorithms that she had to learn.  These less effective algorithms were meant to build her conceptual understanding.  Was it effective?  I really don’t think so.  I don’t think you need alternative algorithms to build conceptual knowledge.  I think you can just build conceptual knowledge with good teaching.

For example, I have no idea how TERC might teach adding mixed numbers but when I look at how to teach this I know that some teachers (most) would teach it by just teaching the algorithm:

2 3/4 + 1 3/4

1.  Add 3/4 + 3/4  = 6/4

2.  Convert 6/4 to    1    2/4

3.  Add the whole number pieces:  2 + 1 + the extra 1 from step 2 = 3

4.  Final answer 3    2/4  or reduce to 3  1/2

 

However, a better approach might be to demonstrate this with a concrete approach rather than starting abstractly with just numbers.

Draw 2 and 3/4 a pies and another 1 3/4 pies.  Show how you can move one piece of the second partial pie to fill up the other partial pie, giving you 3 full pies and  2/4 left over pie (or 1/2 left over pie) – final answer 3 2/4 or 3 1/2.

From here you can now relate the concrete picture to the abstract numbers.

 

This is what I mean by “good teaching” and is much better than using 3-4 additional ineffective algorithms or “discovery” learning approaches.  Discovery learning was something that I was introduced to in my methods class when getting my degree to become a teacher.  It seemed like such a good idea at the time, instead of you telling the student what the answer was or how the problem worked, you devised a lab situation where they naturally “discovered” the solution all on their own.  Since they created it, it was more active learning and hence would stay with them longer than just being told.  The idea sounds great and active learning DOES produce better retention.  The problem is that you have to actually create that situation you are looking for.  If you just give them labs that the teacher THINKS will lead them to building conceptual knowledge but instead just ends up being a lot of extra steps (see the first video example), the impact is the exact opposite.  Our local high school tried this.  They decided to teach Common Core Math 1 concepts through discovery learning.  Instead of giving lectures on exponential functions and showing relationships, demonstrating examples, and having students work problems, they created these lab experiences for these freshmen (and a few sophomores) to do.  The students that I worked with completed the labs but it was clear that they had no meaning for them.  The intent was that this was supposed to build all the concepts they needed about exponential functions when in fact, the students just found answers to questions without piecing together the big picture or linking one lab to the next.  It was an utter failure.  Discovery learning is very hard to pull off.  Not only does it require really good lab experiences but it requires the right kind of student that can learn that way.   Students have a variety of learning styles and many need to be taught by concrete methods, examples, and linking new information to things they already know.

Another important point made by these videos is that it is a waste of time to teach the student the standard algorithm because they will eventually just rely on the calculator anyway.  Is this true?  Well, it is true if we make it true.  It also NEEDS to be true for some students.  If you read my post about accommodations for students with memory problems, they will NEED to have a calculator accommodation because they lack the same ability that the non-LD student has to memorize rote facts.  For this student, I think they do need a calculator so that they can focus more on the big picture and less on things that will never happen for them.  However, what about the student who can learn their multiplication facts but just doesn’t want to put in the time.  What about the 9th grader who still breaks out the calculator for 8×3?  One might argue that we always do have technology at our disposal.  With cell phones that have calculators on them, one is almost never without the ability to use a calculator these days.  Does that mean it is okay to rely on it?  I am a strong believer in technology and feel that we should not be doing tedious problems that one would not do in the “real” world without a calculator, in class without a calculator.  However, for things that one should just “know,” that demonstrates a basic understanding of basic mathematics, yes, students should be required to do these things without a calculator unless them have a documented learning disability.  In other words, let the real world determine the appropriate use of technology in the classroom.

What about the second book that was discussed in the video?  Was it all bad?  I have had students who have used both those algorithms:  the one that uses the place value and the lattice multiplication.  Here are my thoughts on those.  First, I like the idea of showing and having a lab on how 2 digit multiplication can be done with the list of numbers that show the true place value.  This really helps a student “see” what is going on behind double digit multiplication.  In fact, there are other ways that organize it even better that a teacher can use.  We do want to teach in a way that is more than just procedural mathematics.  Not all students will grasp everything but it will help some.  However, this does not mean that the ultimate goal is to leave out the standard algorithm.  The other algorithm is used to demonstrate conceptual understanding, not to be an algorithm that students continue to use.  My student who did try to use this as their only algorithm, did make many more mistakes than students using the traditional algorithm.  As for the lattice method, there is no reason conceptually to show this method.  However, for some students, the organization (keeping things in boxes) helps them from a visual perspective and that is why a teacher might choose to show this.  The student that used this algorithm used it successfully for a long time, he is a rising 9th grader and I wouldn’t be surprised if he doesn’t still use it (I only tutor him on occasion now when he has a test but it is still his algorithm of choice.)  The point of all of this is two-fold: one, use alternative approaches IF it helps a student grasp the concept more and two, allow them to use an alternative algorithm if they can be as fast, as accurate, and as effective with it.  Give the student the choice, it is frustrating when teachers tell students they “have” to use a specific algorithm.  Once a student finds one that meets the criteria of fast, accurate, and effective, they should not be forced to practice other algorithms except in sense of in class concept building labs.

Written by:  Lynne Gregorio, Ph.D. Mathematics Education