RSS
 

Archive for the ‘Education’ Category

Common Core: Integrated Math vs. Traditional Sequence – why the integrated approach doesn’t work

22 Aug

The Common Core Standards were developed and  I am not a fan of common core for many reasons, but that is not the point here.  With or even without common core, there has been a few states that argue that the better way to teach math is using an integrated approach rather than the traditional approach.  Let me define each.

Traditional Approach:  Algebra 1, Geometry, Algebra 2

Integrated Approach:  Take the topics of Algebra 1, Geometry, Algebra 2, Advanced Functions and Modeling, Trigonometry, Probability, and Statistics and integrate them into 3 math classes called Math 1, 2, and 3

The rational behind the integrated approach is that math is integrated in the real world, we model things with mathematics and includes all the topics that one uses in the integrated approach model and our overall focus should be on Modeling Mathematics using the tools of mathematics, not separating out math into separate areas of Algebra 1, Geometry, and Algebra 2.

The above is very true – now let’s look at some other pieces of the picture:

1.  Students struggle with mathematics and is probably one of the most difficult subjects we teach

2.  Can students still learn to model and learn examples of mathematics with traditional approach?

3.  How do students learn?  Students learn best when they stay on the same subject and keep linking new knowledge to existing knowledge rather than jumping from subject to subject.

4.  Do we care more about students actually learning math or the idea of students learning math?   In other words, if method A sounds better but method B produces better results, which should we use?

I would like to see some research studies done comparing student knowledge using an integrated approach with a traditional approach.  Maybe if the integrated approach was done seamlessly, it could produce the desired results but in North Carolina, this is how it is done: (an example of a Math 2 class)

Unit 1:  Geometry

Unit 2:  Statistics

Unit 3:  Probability

Unit 4:  Algebra

Unit 5:  Algebra 1 & 2

Unit 6:  Trigonometry

Unit 7:  Advanced Functions and Modeling (things students used to not see until Pre-Calc like graphing rational functions)

Unit 8:  Algebra 2

The students jump around so much from topic to topic that they don’t make connections while in an Algebra 2 class, they would constantly be working with algebraic relationships and then doing applications of those relationships.  Each unit would have some continuity from the previous unit rather than doing transformations one day and then laws of sines followed by graphing rational functions.  Students struggle to remember everything for the final because each unit is so disjoint from some of the other units.  There is a lot of overlap from Math 1,2 and 3 – students are still doing quadratics in math 2 and they fully covered them in math 1 and although we haven’t started yet, I see them on the syllabus for math 3.

So although the “idea” behind Integrated Mathematics “sounds good” in theory, in practice it is not working, it is not in the best interest of the student as a learner, and I believe that students are learning less mathematics and certainly making less connections.  If I had to learn math that way, I doubt I would have gone on to be a math major, I think I would have been very confused.

These educators forget that those that are meant to go on in mathematics, just WILL, you don’t need to force it.  If you teach them Algebra 1, Algebra 2, and make Geometry a mix of Geometry and some Probability and Statistics, you will continue to have students go on to STEM fields just as we have always had.  Our focus needs to be on doing a BETTER job teaching mathematics in general, not trying to constantly CHANGE the standards, the curriculum, and the scope and sequence.  If we took all the money we spent on those things and put it into putting the really talented math teachers (whose students have said they can REALLY learn from, even those that say they HATE math and can’t do math) with the not so talented math teachers, that is how we would see math achievement improve.

 
 

Paying for college – having multiple children, upper middle class – FAFSA, Timing is everything and It’s Not Fair!

19 Aug

Paying for college is getting more and more difficult, especially for the upper middle class with many children!  I am all about fairness and I never understand when people and agencies fail to see the big picture and provide fairness and equity across the board – this is whether it provides me with benefit or not.

So, one issue I have is with qualifying for financial aid for the middle class / upper middle class and especially for families who have lots of children nicely spaced.  Let’s look at the timeline of how things might unfold for a typical middle/upper middle class family.

  • You fall in love and get married.
  • You attend college (and so does your spouse) – if you are lucky, although I guess this is needed as part of the story but is common to this scenario.
  • You get your entry level job and start making a starter salary, not a GREAT salary but a decent one hopefully or enough to start building the American dream of starting a family and buying a home.
  • So, you have your first child and you buy your first home.
  • You start putting money in your 401K for retirement.
  • You have your second child and you get salary increases, maybe you change jobs a few times which does nice things to your pay.
  • You may have more children – in our case, we had four kids.  You space them out, especially if you have four, who can handle four kids that are all two years apart?  So, some are 3 or 4 year apart.
  • By the time your first one is ready for college, you have built up some nice equity in your home, you have that 6 months of safety cushion the experts say you should have.  You have been thinking about your retirement also, so you may a good strong 401K or other investments.  You may even own a rental property or two, but that is your retirement plan since you are trying to be responsible, after all they don’t give out pensions anymore and health care in retirement is a huge concern.  Your income has grown nicely and you fall in the middle or upper middle income category.
  • Your first child chooses to go to school AND…. you know you have perhaps 3 more children that will follow to put through college as well and you have retirement to think about.  Many families also have someone in the family that is elderly or disabled that they are paying for as well.

You fill out the FAFSA form and look to tell FAFSA about the fact that you have 3 more kids that you have to put through college, all the funds you have now are NOT for just the ONE child… You look to tell FAFSA that you have a disabled child that you will have to support for life, you look to tell FAFSA that your rental properties are your retirement plan and that you chose to plan retirement a little different than just putting all your money into a 401K.  You want to scream at FAFSA that you did it all right, you were responsible and it isn’t your fault that your three kids aren’t triplets and all in school at the same time – you still have to put all three of them through college!  You want to scream that just because you have the savings you are supposed doesn’t mean you are supposed to “get rid of it” and put it into your kids college tuition and now not have the safety net that experts recommend.    FAFSA doesn’t care about any of that, you get nothing, nada, not now and not for the rest of your 3 kids, you get to pay 100% of your kids college costs.  Unless they go to a school that costs $80,000 per year, then they might LOAN you $10,000 and expect you to pay $70,000 per year which you know you could never do.

As an upper middle income family with only ONE child, I am completely FINE with FAFSA saying that I should pay 100% of my child’s tuition.  Yes, I can afford it!  I did, my son graduates in a year and we paid 100% (sent him to a state school that only costs $15,000-$16,000 per year so we could and still afford to send our other kids to college), however, we could could never have sent him to a more expensive school because he has 3 siblings that I have to think about.   FAFSA needs to consider how many kids a family WILL need to send to college.  I understand that not all those kids might go to college so I guess that becomes a problem, so maybe the discount can come as you apply and have already had a kid graduate so you get credit after the fact.  Once I apply for kid #3 or #4, FAFSA can ask, how many kids have you already put through college and calculate that into their EFC.  If I already paid 100% to put 3 kids through school, give me a break on number 4, please, I am not a millionaire, I just want to educate my kids.

 

Choosing schools in Wake County, North Carolina – charter, public, magnet including detailed review Southeast Raleigh High and Moore Square Middle

28 Jul

Which School Do You Choose and Why?  Exploris, Sterling Montessori, Carnage, Apex Middle, Lufkin, Moore Square, Holly Springs High, Apex High, Raleigh Charter High, Southeast Raleigh High, Turner Creek, Olive Chapel, Baucom, Davis Drive, Fuquay Elementary…. 

 

Come explore some Wake County Schools with us…

 

As an educator and a parent to kids who are academically gifted and who have learning struggles and need a 504 plan, I had to choose schools in Wake County for my children to attend.  I have 4 children, 2 have already graduated high school and my last two are in now in middle and high school.  Here is a review, it will be ongoing about some school options in Wake County and a detailed review as we go through the year of the two schools we ultimately chose for our children – Southeast Raleigh High School and Moore Square Museum Magnet Middle.

First, let me address Wake County public elementary schools.  My children have attended:  Turner Creek, Olive Chapel, and Baucom Elementary.

Wake County Elementary Schools:

In general, unless your kid needs an IEP, you will find that most elementary schools in Wake County will be decent and meet the needs of students.  When it comes to giving students IEP’s, however, you will find some schools much more willing to cooperate than others.  For example, Turner Creek is much more likely to give students in need of IEP’s the support they need while Olive Chapel and Fuquay Schools are not.  Many students I tutored who were getting further and further behind academically were not being given IEP’s at their elementary schools and were being given minimal “extra” help.  My own kids also attended Sterling Montessori Charter school and I found they got a very good education there and excellent help if they needed special education services.  From the 3 public schools my kids attended, I would rank Turner Creek the best, then Baucom, then Olive Chapel.

Wake County Middle Schools:

Once your child is ready to start middle school, you may want to consider being more picky about schools in Wake County.  They also solidify their friendship groups in middle school and might not want to their middle school friends (it can be hard enough to get them to leave their elementary school friends) to attend a better high school and this is when I feel making the right choice (think College) really matters.  My kids have attended Apex Middle School, Exploris, Sterling Montessori, and now I have one who just started Moore Square.

Davis Drive Middle is the one middle that I have found really stands out as a GOOD public middle school.  Families specifically buy houses so they get put in that district.  The kids I tutored that attend that school are very bright and I don’t get much in the way of teacher complaints, so Davis Drive gets a Thumbs Up.

Lufkin Road Middle does not have the best reputation.  I have had heard lots of complaints of not-so-great teachers at the school.  Apex Middle seems to be a little better than Lufkin.  My son did not like the school at all but he left a Charter school to attend so didn’t go in with a bunch of friends he had known since elementary school.  These public middle schools seem to have a lot of boy-girl focus so be prepared for that.  None of them are terrible but none of them are particularly great (outside Davis Drive) either.  One  problem is that they don’t do much for AG kids.  The base schools have very few electives and are just average schools – if we were to grade them, they would get a C.

The middle school at Sterling Montessori is NOT as good as the elementary school.  It is not that organized but I would still say it is probably better than a school like Apex Middle or Lufkin.

 

Exploris middle school is a good school overall.  I was very impressed with it in the 6th grade when Kevin was the director.  The new director has changed some things and seems to be putting much of her time into growing the school that it seems that the things that made it so good in 6th grade decreased, which is a shame.  Before, my son would go out to downtown Raleigh field trips and museum experiences ALL the time.  In seventh grade, he went significantly less.  In eighth grade, they piled on the work and I felt their academic choices were more obscure random things than core topics that would serve him well and prepare him for high school.  We chose to leave part way through 8th grade, in part since the program seemed to be lacking all the good things that it had, some bullying was going on that was not being addressed, and because his class was filled with so many kids with “issues” and he had some of his own that he didn’t feel connected with anyone after 2.5 years at the school.

I will review Moore Square below since this will be a review I will add to since my daughter just started there.

Wake County High Schools:

This is where I think parents really need to pay attention to where they send their kids.  Many of Wake County high schools are doing a poor job of educating kids.  Since I tutor mostly high school kids, I have worked with kids from many of the different schools and have just been appalled at what I have witnessed.  Here are a few examples:

  • Teachers allowing kids to cheat because their students are failing and the teachers need to kids to pass to make the teachers look good
  • Teachers who don’t bother to grade papers, just give a random grade and/or 100 – and throw the papers in the trash rather than return to student with feedback (since they weren’t graded)
  • Teachers who don’t get around to teaching most of the period, tell stories, go outside, etc. but still test students on material they haven’t taught
  • Teachers who assign homework but don’t clearly communicate to the students what it is so the students have no idea what to do
  • Teachers who give assignments that they know kids will and have cheated on and then count it as 2 test grades (F kid scores 100) so they can pass the kid
  • Schools that give diplomas to kids who have not met all the requirements to graduate or they “boost” them / falsify information to allow them to graduate rather than helping student learn and really earn diploma
  • Teachers who grade unfairly because they just don’t care
  • Teachers who don’t respond to parent emails and request for help with their child
  • Schools that ignore 504 plans and IEP’s
  • Schools that require students to meet requirements for graduation and then don’t offer those requirements so student can’t get diploma (special education)
  • Schools with no follow through on discipline so kids don’t have any consequences and just continue to do whatever they please
  • Schools who let their students knowingly smoke in a spot right near the school in plain sight of cars driving by
  • Teachers who give out passing grades to failing students just to move them forward and then the student is just further behind in the next class, especially in math
  • Students who are left alone for almost all period when subs don’t get there until the last 20 minutes of a 90 minute period and no teaching happens with any subs

If you want your kid to get good grades that are deserved, learn what they need to, and be prepared for college, you need to really consider what high school you send your child to.  The above examples, FYI, come from Apex High School (most of them), Holly Springs High, Athens Drive High, and Panther Creek High (although overall Panther Creek has a fairly good reputation compared to these other schools.)    Most of the teachers in these schools are burned out and are passionate people that care about your child’s learning.  I am sure this is happening in other schools across Wake County as well.

My kids have attended (for high schools) Apex High School, Raleigh Charter High School, and  Southeast Raleigh High School.

Apex High School – I will not send my kids to Apex High anymore.  My oldest only went there for 2 classes as he went to Raleigh Charter most of the time.  He had a decent teacher for AP Environmental Science (scored a 4 on AP exam and got college credit) and a not so great English 4 teacher.  I am so glad he did not have to take math there.  Most of the math teachers there are terrible.  My other son was in the OCS (Occupational Course of Study) so he was not in regular education classes much.  The school had a requirement that he do 360 work hours that they told us they would provide for him to graduate but then didn’t provide them.  We had to go to mediation and get them to provide a place for him to volunteer over the summer to get the rest of his hours in so he can get his diploma.  We told them it was like requiring English and then never offering it, not acceptable.

Raleigh Charter High School – is a great school if your kid is book smart, is willing to study a lot, and very academically minded.  It is not for the “average” kid.  Most of the kids there aren’t into dating boy/girl relationships, they focus on studies.  It was interesting to see the huge difference between a public MIDDLE school which had all this boy/girl dating focus vs. RCHS which was not that way and the kids were in high school.  My son liked it there but we also know he was the right “fit” for that school, some of my other kids would not be.

So, we decided to apply to two magnet schools for my youngest two kids for middle and high school.  With lots of experiences with schools from the older two and all the kids I tutor, it will be interesting to see how they compare.  I will start my review and add to as I go through the year.

Moore Square Museum Magnet Middle School – Parent Review – School Year 2014-2015

First impression – VERY GOOD!!  We first met Mr. Bass, the principal, at the magnet fair and I instantly liked him.  When we met other principals / students / teachers at other magnet schools, we just didn’t get impressed.  In fact Carnage didn’t even talk to us, I had to say, “hey, can you tell me about the school,” then I got a few simple statements from a student and she stopped talking… if they are going to send kids to represent the school, they need to send good ones!

Second impression – VERY GOOD!! – in fact, so far, every time we have been invited to learn about something with the school it has been amazing.  Their orientation was the most organized, intensive, educational orientation I have ever been to.  So much so, that I will probably write a letter to Mr. Bass letting him know that so he makes sure he keeps up the good work.  We went to Lufkin’s orientation one year when we though our son was going before he got into Exploris and it was so weak compared to what we got at Moore Square!  I hope all this organization and thoroughness that we see is a sign of how the school is run when kids are there!

The only negative to report was that we had to rate all my daughter’s elective choices and only one out of 58 was selected for her first two quarters!!!  I was not happy.  However, we will go with the flow, they did change her schedule when I put in a request saying that she did not want Dance or Pollution Solution and they changed her to Film and an Art class and she seems happy with that.  My daughter is now in quarter 3 of 6th grade.  The school provides VERY TIMELY reports on her grades, we get an interim every 3 weeks and things are put in powerschool daily.  Her teachers, overall, seem very good.  She has a decent amount of homework, but that is expected in middle school.  Her math teacher seems a little scattered and not that organized and although she is getting A’s, I hope she is learning everything she needs to since she will be taking High School level math in 7th grade.  There has been a great number of choices for electives that have been interesting and she has always gotten things that are decent and reasonably high on her choice list after the first semester and she did like her first semester electives.  One of those electives was a computer class that was required of all middle school students, anyway.  I think maybe there was a fight once but I have heard of more fights and issues from her friends at Apex Middle than she has had at Moore Square.  She is in classes with all other AG kids, except electives which is a mix of all grade levels but she usually has some friends in her class with her.

Southeast Raleigh Magnet High School – Parent Review – School Year 2014-2015

We weren’t really sure if this was going to be the right fit but we went and observed and I was very comfortable, felt safe, and really liked all the teachers.

Orientation – was terrible for parents – they did not tell us anything important and just asked for money – art boosters, athletic boosters, pta – they need some lessons from Moore Square!!  My son had a good time at his orientation though.

We did need to meet ahead of time with my son’s counselor to make a 504 plan and all of my son’s new teachers were at the meeting.  It was a great meeting and we were very impressed.  They were very accommodating to his needs (even more than Exploris – although that was again from the new director, Summer, the previous director had been very accommodating.)  It was the best 504 meeting we have ever had.  His PE and Engineering teachers were very lively and fun and full of support and information regarding everything.

First day of school went very well for him.  He made friends easily, the student leaders from his orientation remembered him by name and said hi.  Everything was very positive.

Freshmen have to take World History / English as a combined class that lasts a full year and the rest of their classes they take as regular block classes.  They also usually try to put freshman in Healthful Living and get that out of the way Freshman year.  Kids who are magnet kids are often in the academies:  Engineering, Biotech, or Information Technology (Computers).  Those in the academies must also be in New Tech (project based learning) or if you are not in an academy, you can still sign up for new tech classes if you want.  They do put all the academy kids in the same classes but not necessarily all the engineering kids in the same class – mostly because these are the new tech classes they have set aside and you must do new tech if you are in the academies.  I think the new tech classes are great anyway, it takes the focus on just putting all the focus on content knowledge for your grade.  Kids do both tests and projects and get points for handing in work, working well with their group, creativity, grades on tests/quizzes/projects, etc. but only half of their grade comes from actual content knowledge (scores from the test grade or content knowledge from project grade) – so kids have a lot of ways to score points in a variety of ways and this helps give a more realistic picture of their ability as a whole and is graded more like a work environment than just, “can you memorize facts.”

Overall, the teachers I have met at the school have been excellent.  Some are better than others and some are off the charts, amazing!  In general the quality of teachers that I have met up to this point, far exceed the quality of teachers I saw at Apex High School.  They seem to want to be here, willing to work with parents / communicate with parents, and help children learn and excel.

The amount of technology this school has is also incredible.  In the new tech classes, each room has a computer for each student.  In the some of the specialty classrooms, like Digital Arts, the room is filled with Macs with huge screens and the latest Adobe Suite for learning, they are not behind in their software like other schools (at most they are one version behind).  The type of electives the school offers if your child is interested in engineering, biotech, computers, digital arts, etc. is amazing.

They have great clubs and teachers that support those clubs.  They have a wonderful Robotics Team and the Theater director is the most enthusiastic, fun, encouraging person you will ever meet!  My son has blossomed at this school.  The big question, everyone is worried about, is it SAFE?  The answer is YES.  There may be some “bad” kids, I don’t know, we haven’t met any!  I am sure there are “bad” kids at every school but the fact that they don’t stand out in anyway or anymore than any other school shows that this school is no different.  There are not fights, the kids seem respectful and nice.  My son is involved with so many activities that keep him at school until 9:00 pm at night and gone to football games – there has never been a problem.

 

Express Bus for Magnet Schools in Wake County

One of the downsides to magnets is the lack of neighborhood busing.  We were going to drive our kids to school the first day but the transportation and school personnel suggested that letting them ride as soon as possible is best since that is when they will help students learn which bus they need to take, etc.  We also know that they will be shutting down some of the highway soon for repaving, so riding the bus will optimal.  I was pleased that our bus doesn’t seem to leave too early.  I didn’t really want to have to put them on a bus at 5:45 and I know some people do.  I think if we did, we would drive to a later stop or drive.  Our bus doesn’t come until 6:20-6:25 and the stop is only 5 minutes from our house.  Right now, we are planning on leaving at 6:05, maybe later we will see if 6:10 will work once things get more predictable.  The kids are on the bus for only 30 minutes and there is only 1 other stop.  All the kids on the bus seem like nice kids.  There is a mix of middle and high school kids but they have the high school kids in the back and middle school up front.  Most high school kids are only 9th and 10th graders since after that, they can drive.  I guess putting my 6th grader on a bus with 9th and 10th graders doesn’t bother me since her brother is a 9th grader and on the same bus.  They take the bus to Southeast Raleigh HS, then my son gets off and goes into school.  He is there on the early side since the buses have to get there early enough to get the rest of the kids off to their schools.  They usually arrive by 6:45.  This will give him time to listen to music or visit with friends (which is probably going to be what happens).  My daughter catches another bus to Moore Square.  They had no trouble at all.  They didn’t get home until 3:38 today (first day) but they have to make sure they have all the kids in the first week or so, therefore it takes longer.  Later, they should leave SE Raleigh by 2:40 and be back by 3:10.  We feel good about the bus and our plan is to keep the kids on the bus.

 

Do you have a Review of a School you would like to do?  Send it to me and I will include other family reviews for any schools located in Wake County.

Try to include what you like about them and what you don’t like about them.

If you have any questions about the schools we have reviewed or mentioned, please ask,.

 

 

 

 

 

Summer Math Preparation for the Common Core Student Grades 4-8

28 May

Recently I have been working with some students getting ready for their End of Grade Testing in North Carolina.  This is a couple years into our adoption of Common Core.  I have watched Common Core unfold and found both positive and negative things about the new standards.  This is not an article about those!  However, one of the big negatives is that students are spending more time on “conceptual” understanding and “alternative” (and long winded) approaches to mathematics that are getting further behind on the basics including the ability to do procedural mathematics.  In the mathematics education community, there has always been much discussion about the percentage of focus on procedural mathematics vs. conceptual mathematics.  Let me quickly summarize the current thought:

Procedural :  the ability to perform mathematics and solve actual problems such as 4X3 and 1/3 + 4/5.  Procedural mathematics gets a bad wrap, many educators assume that since calculators and computers can do this, our focus needs to be on the concepts behind the procedures and if we do this, the procedural math will come naturally.  This DOESN’T happen!  So many students can’t do the procedural math steps and we don’t spend enough time on them.

Conceptual:  the ability to understand the concepts surrounding the mathematics and the “why.”  One cannot solve a word problem involving multiplication if they don’t understand the concept of what multiplication is and how it is different from addition or subtraction.  However, one still needs to be able to do the procedural steps to get the answer to the problem and I disagree that the “procedural mathematics” will come automatically if a student knows the concepts.  Often, students only get to a partial understanding of the concepts and then they are in a real bind since they can’t do either the procedural or conceptual.

So, how does this apply to YOUR child?  Well, most children are just not given enough time practicing the procedures and this is what a parent must make up at home until these steps are automatic and easy.  Leave the conceptual teaching for the teachers (or get a tutor if needed for this) but you can do your child a huge service at no cost by having them master procedural mathematics!

This is not an inclusive list but a list of things that one should work on at each grade.  If your child is in 6th grade and hasn’t mastered the objectives listed for 4th grade, you need to start there.  Start at whatever level your child is not 95% successful at.

Grade 4:

  • Knows all multiplication and division facts (0-12)
  • Can do multi-digit multiplication
  • Can do long division with a single digit divisor
  • Can convert between mixed numbers and improper fractions

Grade 5:

  • Can add, subtract, multiply, and divide with fractions with unlike denominators (including 3 or 4 in a row)
  • Can add, subtract, multiply, and divide with mixed numbers
  • Can reduce fractions (including BIG fractions)
  • Understands divisibility rules and how to apply them (minimum can do 2, 5, 9, and 10)

Grade 6:

  • Can add, subtract, multiply, and divide with decimals
  • Can convert between decimals and fractions
  • Can solve 1 step algebraic equations
  • Can combine like terms in algebra
  • Can use distributive property in algebra
  • Can solve order of operation problems
  • Can find the 5 point summary for a box plot, graph, and interpret
  • Understands / memorizes appropriate math vocabulary:  mean, median, mode, range, IQR, Q1, Q3, variation, cluster, gap, outlier, MAD, standard deviation, spread, radius, diameter, etc.

Grade 7:

  • Can set up and solve ratio and proportion problems
  • Can set up and solve percent problems from words
  • Can solve 2 step algebraic equations
  • Can simplify algebraic expressions that mix distributive property and combing like terms
  • Can convert from words to algebraic expressions
  • Can solve 2 step algebraic equations that involve fractions and decimals
  • Can find volume and surface area of prisms
  • Can find area, perimeter, and circumference of mixed figures

Grade 8:

  • Can find slope from 2 points
  • Can find equation of a line from a slope and point
  • Can find equation of a line from 2 points
  • Can find equation of a line from a table or graph
  • Understands and can apply idea of x and y intercepts graphically and as points
  • Can find lines perpendicular to other lines
  • Can apply Pythagorean theorem
  • Can find the distance and midpoint between two points
  • Can solve more advanced algebraic equations including ones with fractions and decimals
  • Can solve problems involving the use of all exponent rules including negative exponents

 

I suggest that each student does 4 problems every night, this way they are not overloaded but they are doing math consistently.  They can’t move on until they are getting answers consistently correct and then always revisit old problems with new problems.  For example, your child might have mastered addition and subtraction of fractions with unlike denominators and they are working on multiplication and division of fractions now.  Some nights they will get all 4 problems of multiplication and division but some nights they will get a mix of old, one of each operation or even older material, one adding fractions, one dividing fractions, one long division (grade 4), and one reducing fractions (application to long division).

This IS the best way to help your child be successful.  Always check your child’s work after the first problem, you don’t want them doing all 4 problems wrong, then they are practicing how to do things wrong!  If it looks good, they can continue.  If they don’t get all answers correct, give them the first chance to fix it, if they can’t, then you can help them out or save up the pages and meet with a tutor and do these problems with a tutor.

Go to sites where they print out worksheets for your child and answers for you!  Sites such as math aids  and Kuta software.

Lynne Gregorio, Ph.D.

Mathematics Educator

 
 

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.

 
 

Single Subject Acceleration Wake County Public Schools North Carolina (Math and Language Arts)

19 Feb

Many parents may have questions about single subject acceleration.  First, what is it?  It is a program that allows students who are advanced in math or language arts to work one grade level ahead in that area while still remaining in their current grade.  How is it different from grade advancement?  Grade advancement requires that the student be able to prove they can work at 2-3 grade levels ahead in every subject in order to be skipped a grade (per Wake County schools).  Other school districts do things differently and I have friends who have done grade advancement and they did not have the 2-3 grade level bar to reach, more like at least 1 or 2 grade levels.  It is very difficult to get grade advancement in Wake County Schools.  My own child was tested and scored 2 grade levels ahead but missed one test criteria by 2% so they denied her grade advancement.  The bar was not really appropriate, why does a child need to be 2-3 grade levels ahead to work 1 grade level ahead.  That is a whole different blog, however, this one will focus on single subject acceleration.

My daughter does do the single subject acceleration.  When she first started, there was no procedure in place for identifying kids for this or tests/hoops they had to jump through.  However, with the implementation of common core, they now test children and/or have to show portfolios of work.  This all has to be presented to the same committee that approves the whole grade advancement and the new process is somewhat similar now to that process.  It probably keeps some children who are capable out of the program.  Since my daughter was already in the program before the start of these new rules, she was grandfathered in.

In second grade, the principal did not approve of putting children in grade advanced classes so my daughter just did independent work.  In third grade, she changed schools and was put in a 4th grade math class.  In fourth grade, she went to a fifth grade math class and this was the first year of common core math.  She did not have any trouble with the transition from the less rigorous math to the fifth grade common core class.  However, there some things to point out.  First, she took the Case 21 tests for her grade and the advanced grade but she only took (and this continues to be the case) the EOG for her real grade, not the grade that matches her math class.  This does cause some issues since she isn’t as “fresh” on some of the topics from a year ago, however, since math is mostly cumulative, she still does well.

The big change came when she went to fifth grade.  The school system held a meeting for all of us parents to tell us what we could expect.  All 5th grade single subject accelerated kids (math and language arts) would do online courses.  So, my daughter sits in front of a computer (on her own with no teacher) and listens to videos of a teacher giving lessons.  The video teacher assigns homework, my daughter is expected to do her homework (no one checks this) and then check her answers the next day with the new video.  The online teacher tells how to solve each problem from the homework.  She has “quick checks” where she will do online questions to see how she is doing every few days.  Each unit has a quiz and then a test.  The units come with a review sheet that is like the test but with different numbers so she knows what to expect on the tests.  It has only been with my help (and getting some C’s to start) that she has learned that she has to redo the review sheet a couple times to make sure she understands every problem before a test (now she has been getting A’s).  She is also allowed to retake tests if she wants to and did that with some of those C’s.  The material isn’t always printed out for her though and she can be ready to take a test but doesn’t get it for another week so she is already on to her next unit and still hasn’t taken the previous units test.

The units are broken down by days but no one really makes sure they are on the right day and she is often behind by the end of the quarter.  Sometimes we have to cover a few days at a time to catch her up.  We also found that as a 10 year old, it was a lot to ask her to do her homework on her own with no one checking up on her and not revisiting the problems she got wrong to then make sure she could do them correctly.  Hopefully, the majority of these kids are very bright and very motivated because doing this online course on your own at 10 is a lot to ask.  My daughter and I do it together every day and I make sure she understands the material.

The math course itself is Common Core Math Six Plus (basically Honors Sixth grade math) – it covers all of 6th grade math and 1/3 of 7th grade math.  The content in the online course is TOUGH!! I think it is harder than what kids are getting in the regular classroom.  I am not sure if they get the same packets, maybe they do, but I know kids in regular 6th grade math (not the plus) have it much easier.  Some of the algebra expected is quite challenging and my daughter just finished this unit on surface area and volume that was so really tough.  In fact, if you gave some of the review sheet questions to high school students, they wouldn’t be able to do them!

The units they cover deal with arithmetic, integers, percents, ratios/proportions, surface area, volume, transformational geometry, algebra, algebra word problems that require you to build linear equations (wow!), statistics, advanced perimeter and area, coordinate system and coordinate geometry, measurement conversions, exponents, scientific notation, and more!

These are not basic questions about these things, the percent questions are the type of question you would have seen in an Algebra 1 class before, they are doing real algebra, the geometry involves surface areas of triangular prisms and square pyramids, area involves area of mixed shapes including missing sides, rectangles, circles, half circles, and more.  This has been a real challenging course for my daughter and it has been at JUST the right level for her.  Finally, something that isn’t too easy or too hard but I understand why WCPSS doesn’t want just anyone taking this class at 10 years old!  On the other hand, some of the content at the younger years still moves too slow for many kids even if they aren’t ready for single subject acceleration so it is unfortunate that there isn’t anything in between!

At the meeting, we were told that in 6th grade – the students will take 7th grade Common Core Math Plus and then in 7th grade move into Common Core Math 1 (high school math).  The problem I see is this:  when looking at the online 6th grade math plus class, it is advanced and challenging but when looking at the 7th grade Common Core Math Plus, it repeats a lot of the content in the 6 plus class but just adds a twist in each unit.  I am tutoring a student in CCM 7 + now and he is not doing too much more than what my daughter is doing.  In fact, she has a deeper understanding since the online class is so rigorous.  So, I think she is going to be “bored” next year.  She probably won’t mind that, though.  The problem then comes that the following year she takes a huge leap into CCM1 high school math.  There is not a good transition from CCM7+ to CCM1.  For students making the leap from 7+ to CCM1, there should be more of a prealgebra class, this would be far more helpful than the repetition I believe she is going to get next year.  The other thing we were told is that most middle schools won’t have CCM2 offered for 8th graders so she will be back to taking an online class in 8th grade.

As for those in Language Arts, they put in an enrichment class, so at no point does your child actually get to take high school English 1 prior to high school.  Instead, their 8th grade language arts is just an enrichment online class and then they are back in with everyone for Honors English 1 in high school.  It is unfortunate that they can’t take English 1 early if they are grade accelerated like the math students can.  Math students get 2 years of high school math finished in middle school.

I hope this is helpful for those looking into how SSA for WCPSS works and what it means for math and language arts.

 
2 Comments

Posted in Education

 

Help, my third grader can’t write! Creative help for kids who hate writing.

25 Jan

Let’s talk about kids and writing.  Lots of kids, especially boys, dislike writing intensely.  Some children find it physically painful to write a lot.  Some find that their thoughts come to them too fast and they just write run on sentence after run on sentence.  So, what are some creative ways to help a young struggling writer?

  • First, make sure the child understands the main parts of a sentence.  They should understand what a noun is and what a verb is.  You can tell them a noun is a person, place, or thing while a verb is an action or “state of being.”  The “state of being” is a bit hard to explain but with examples such as showing them “is” and “am,” they will catch on.  It is okay if those come a little slower, just keep reminding them.  Have students show you what the subject of the sentence is, what the verb is, and what the predicate is (or the part that follows the verb that closes the sentence.)  For example:  The boy ran to the store.  The child should be able to say the “boy” is the subject and is a noun.  “Ran” is a verb, talk about how running is an action, and the rest of the sentence talks about “where” he ran… “to the store.”  Keep dissecting simple sentences until your child catches on.  They won’t mind this as much since it isn’t writing, it is just talking about sentences.  
  • Second, introduce them to the idea of “fat” sentences.  Talk about adjectives and adverbs and conjunctions to make a sentence more interesting and complex.  A good game to play is that one person draws a picture (I like to use a white board, kids find them fun) and the other has to make a fat sentence about the picture.  You take turns.  My daughter and I had silly pictures and silly “fat” sentences.  A “thin” sentence would be, “The boy ran to the store.”  To make that a fat sentence, we would say, “The red-haired boy in a blue shirt ran quickly to the store that was about to close.”  You can talk about how you added adjectives such as “red-haired” and a description “blue shirt” and an adverb, “quickly,” and finally you elaborated on the store information, “it was about to close.”
  • The above game is nice because we just write ONE sentence at a time and we make sure we include correct capital letters and punctuation.  If spelling is an issue, for now, just help your child rewrite the word spelled correctly.  Spelling should be taught separately from writing so you should be having spelling lessons, they link well with phonics lessons as they learn the rules of the English language such as letters like /c/ have both a hard sound and a soft sound.  You usually will see the “magic e” when the /c/ makes its soft sound like in “ice.”
  • Next I would have a talk about commas.  We don’t teach comma usage early enough.  A young child doesn’t need to know all the comma rules but I would suggest they know these:  Commas after sentence starters such as:  In the beginning, the cat was upstairs.  Before school, I went to McDonalds.  Point out that the subject is not in the sentence starter but after the comma.  Next, they should use comma’s to separate items in a list such as:  I like apples, bananas, and grapes.  Third, they should use commas to “double name” someone or something.  My friend, Jill, likes popcorn.  We already said who likes popcorn, “my friend” does but we also said who “my friend is” so we double named the subject here:  my friend = Jill so Jill must be set apart with commas.  The last thing I would teach is quotation for when your child wants to make people talk in her stories.  Teach the location of commas and quotes:  “Hey, I will go to the store with you,” said my friend.  My mom called me from the stairs, “Sarah, it is time to go.”  You can teach these with worksheets where the student just adds the punctuation so it isn’t a lot of writing.
  • Now the fun part.  Notice until now, your child hasn’t had to actual write anything more than a sentence.  Our next step is to get the child to write many sentences.  Tell the child we are going to write about something, say dogs.  Tell them they have to think of 5 sentences that talk about dogs.  Now, get out your phone, ipad, or computer and use a voice dictation app.  Dragon Naturally speaking if a program you can buy for the PC or you can get Dragon dictation for a tablet or phone.  You can also just use your text message area or speech to text in an email on your phone, whatever is easiest.  Teach the child to talk with punctuation, speech to text will understand this.  You give an example about cats.  You say, “Cats are a lot of fun period.”   You actually say the period and the word comma if you are using a comma – out loud and program will know to put in the punctuation and not the word so the above should read, “Cats are a lot of fun.”  It forces the child to stop between sentences since they have to say, “period” before they can go on to their next thought.  You would continue, ” I have two cats comma their names are Lill and Bowser period.”  This will come up as “I have two cats, their names are Lill and Bowser.”  You continue, “Bowser is the black cat and she likes to sleep with me period Lill is the more playful cat period I think cats are great fun period.” After their dictation is over (you may need to pause and do one sentence at a time if your child doesn’t immediately know what his next sentence will be), you look at it together.
  • At this point, you would talk about making sure you vary the start of your sentences.  If your child said, “I like dogs period I like to throw  a ball for my dog period I like to pet my dog period I feed my dog dinner at night period.”  You can actually write out the sentences for the child and underline, in color, the beginnings of the sentences and how they all start with “I” and most start with “I like.”  You can tell the child that you don’t want your sentences to all sound the same so you need to vary the start of each sentence.  You can model it for him, “Dogs are great.  My dog likes it when I throw his ball for him.  Sometimes, I will rub my dogs belly.  It is my job at night to feed my dog dinner.”
  • These last two steps will take some time until the child can write a good 5 sentences that all stay on topic and have different sentence starters so get that strong before you move on.
  • After that is going well, you can begin to introduce the idea of making some of the sentences fatter and more interesting with details like you did in the earlier game.  “Dogs are great, there are so many different colors sizes, and types of dogs.  My black and white dog gets very excited when I throw his yellow tennis ball for him.  Sometimes, I will run his belly, he lays very still and enjoys it whenever I pet him.  At dinner time, my dog is hungry and it is my job to feed him.  He is always very happy to get his food.”
  • You can see how each step we just add a little more expectations.
  • When you are now able to get fat sentences, good mixed starters, and more complex sentences it is time to begin to talk about organization.  Let the child know there needs to be a topic sentence that is GENERAL that will tell the reader what they are going to be reading about.  Give examples for your child to choose from:  Which is a general topic sentence and which is a smaller detail?  A)  Dogs are fun and great to have around.  B)  My dog likes to chase a ball.  OR  A) When my room is clean, it is easier to find things.  OR B)  Clean rooms have a lot of advantages.
  • Now work on making a writing organizer to help with the structure of writing.  Come up with a GENERAL topic sentence and then add 3 details with examples to support the topic sentence.  The organizer doesn’t need full sentences, just jot down ideas to remind you what you will talk about.  For example:  Dogs are fun and great to have around.  (Topic Sentence) – the details would be “Why are they fun and great to have around?”  1)  Play ball 2) cuddle and look cute 3)  always there for you.  Now you have your topic sentence and three ideas you can go back to writing sentences, it is okay if the first ones are skinny, after you write them once, go back and make them fat.  “Dogs are fun and great to have around.  One fun thing I like to do with my dog is to play ball.  I throw the ball over and over and he keeps bringing it back until he gets tired.  He even jumps for it and catches it.  My dog will also cuddle with me on the couch.  He looks so cute when he is all snuggled up to me.  He lets me pet him for hours and loves it.  Sometimes people get lonely but your dog is always there for you, there is a reason they say “Dog is Man’s Best Friend,” because your dog is always there for you, no matter what. ”  This might be a little advanced for a third grader but it is also good to show them models of what you are looking for and how you met your goals of:  Topic sentence, 3 ideas that support the topic with examples, unique sentence starters, and fat / complex sentences.

There are many additional steps you can take from here but this is a great start!  Happy writing / Happy Dictation.

 

Written by:

Lynne M. Gregorio, PH.D.

http://www.apex-math.com

 
 

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.

 
 

Common Core Math – Algebra 1 in the 6th grade, is your child ready?

20 Nov

When did you start Algebra for the first time?  The majority of adults will say 9th grade.  Some students who were advanced might have taken it in the 8th grade and even done Pre-Algebra in the 7th grade.  This was the case for me.  I was considered on the advanced track and took 7th grade Pre-Algebra, 8th grade Algebra and was taking Calculus my senior year.  I loved Algebra, it came naturally to me when I started learning about it in the 7th grade.  I don’t really remember too much what I did differently in Pre-Algebra vs. Algebra, especially since I had a whole year of it but given we had a year, we went very slowly which allowed me to develop strong math skills.  Keep in mind that I went on to get a Bachelors degree and Masters Degree in Mathematics and then a Ph.D. in Mathematics Education so I am a math minded person.  If I was in school these days, things would probably have turned out very different for me in mathematics!

Our old curriculum, prior to Common Core, in North Carolina had students doing middle school math which consisted of a mix of Geometry, Arithmetic, Probability, and Statistics.  They began to explore a little bit of Algebra in the 7th grade and much more Algebra in the 8th grade.  They repeated all these Algebra concepts again in the 9th grade when they officially took Algebra 1.  Of course, a few students would be on a track 1-2 years ahead of that schedule.  Some schools pushed students to go the 8th grade Algebra route and others held students back for fear they were pushing them.

The new Common Core curriculum has changed the scope and sequence of middle school quite a bit.  Students begin learning quite a bit of Algebra 1 in the 6th grade.  This is for ALL students, not just the advanced students.  Sixth grade math has students multiplying with exponents, using the distributive property with variables, combining like terms, solving 2 step equations, writing algebraic expressions and even coming up with linear functions from word problems.  This is pretty advanced stuff and very abstract.  For your above average student, it should not be a problem to master.  The average student may struggle trying to learn these Algebraic concepts at age 11 and those who are already not strong in math, will be totally lost and this will start their spiral towards mathematical failure.

Should your child be learning Algebra 1 concepts in 6th grade?  Is he or she developmentally ready for it?  Does he have a strong background in arithmetic and the prerequisites that come before beginning to master Algebra 1?  I believe there are MANY children that are NOT yet ready for this leap and that it is a disservice to them to put them in a class with these standards before they are ready, setting them up for failure.  Why do we remain opposed to “tracking”?  There needs to be levels for students and Common Core 6 might be a reasonable goal for 75% of students (maybe – that high, I am being optimistic) but the other 25% deserve to be in class that fits their developmental level and allows them to master concepts and basics before pushing them into these advanced Algebra concepts at such a young age.

My own children are advanced math students, so I feel it is important to consider both ends of the spectrum.  Students do not stay together based on age in mathematics, they begin to divide early and we don’t seem to accommodate this, causing so many students to hate math, feel like a failure in math, and be unsuccessful.  If instead, we just were willing to step back and let some students move more slowly through math while let others move more quickly, many more students could have success in math.

As a math educator, I would rather have 100% of students MASTER their classes even if 25% get to Calculus, 50% get to Pre-Calculus, 30% get to Algebra 2 and only 20% make it through Geometry by graduation but they all have mastery of math to that level than what we have now which is requiring all students to take courses equivalent to Algebra 1, Algebra 2, Geometry, and another math but at a mastery level for some as low as 20% in these courses!

I continue to express my dislike for Common Core Mathematics but not for the reasons so many others dislike it (political, etc.) but for the lack of appropriate education and expectations it has for students.

Written by:

Lynne Gregorio, Ph.D.

 
2 Comments

Posted in Education

 

Common Core Math 2 North Carolina Scope and Sequence

19 Nov

As Common Core Math becomes more widely used and debated, I continue to analyze the effectiveness of this new curriculum.  The traditional approach of teaching mathematics in high school was to teach Algebra 1, Geometry, Algebra 2, Pre-Calculus (or some type of equivalent such as a Functions and Modeling Class), and then Calculus / Discrete Math / Probability and Statistics.  You may wonder what the reason was for putting Geometry between Algebra 1 and Algebra 2.  My personal belief from experience is because students need to have a certain level of mathematical maturity to be able to handle topics in Algebra 2.  Geometry is usually an easier class so following the order Algebra 1, Geometry, Algebra 2 allows students to work in a progression from easier to harder and develop mathematical maturity along the way.  In fact, one school in our county tried switching to Algebra 1, Algebra 2, then Geometry for a year and found it didn’t work as well so they switched back.

With the new Common Core, states have the choice of implementing the standards with a traditional sequence such as Algebra 1, Geometry, Algebra 2 or doing an integrated approach which mixes topics into Integrated Math 1, 2, and 3.  North Carolina chose the integrated approach.  In Common Core 1 (Integrated Math 1), students learn a few units on Statistics and then focus mostly on Algebra 1 topics.  However, when they take Common Core 2, the students are taking a course that is almost all Algebra 2 concepts with even some concepts from Advanced Functions and Modeling (the course that would follow Algebra 2) added as well.  Very little Geometry is introduced in Common Core 2, it is almost exclusively a course on functions.

The first unit deals with transformational Geometry where students learn about reflections, rotations, and translations.  They also spend time just barely being introduced to the idea of congruent and similar triangles.  They do some review of distance formula, midpoint formula, midsegment of a triangle, and then the focus shifts to Algebra 2 topics.  The second unit deals with quadratic equations including converting to vertex form by completing the square, finding the x and y intercepts, and graphing.  There is a huge focus on translations of functions, starting with quadratics but moving into translations of every function type you can think of.  The third unit deals with radicals, rational exponents, solving exponential equations, solving equations with rational exponents and radicals.  Students solve equations by converting to the same base and using logs.  Students must understand, compute, and use inverse functions to solve equations and graph.  Students also do applications of exponential equations such as half-life and compound interest.  In the following unit, graphing becomes the focus again.  Students use translations and graph rational functions, greatest integer functions, absolute values, square root functions, cube root functions, cubic functions, log functions, and probably a few others I can’t think of.  They also solve rational equations and work with inverse variation.  The last unit deals with probability including permutations, combinations, independent and dependent events, and sample spaces.

You can see that these topics are rather advanced and that a student who is not a strong math student that tries to take this in their sophomore year (the year that most students who are not advanced would take it) are likely to struggle, especially given that North Carolina grades on a 7 point scale.  Whenever I talk to students that I tutor in this course, I constantly get reports that at least half, if not more, of their class is failing.  However, teachers will most likely give the student a D and move them along.

So many people complain about the political problems with Common Core and how it was started and funded.  I have no issue with that, my issue with Common Core is that we are not thinking about what students are developmentally ready for or putting a plan in place to help students actually succeed in this new curriculum.  Students start doing Algebra 1 in the 6th grade now with Common Core.  In 6th grade, students are required to learn how to solve 2 step equations, multiply variables, use the distributive property with variables, combine like terms with the distributive property as part of the problem, write algebraic expressions from words, write linear y=mx+b expressions that model real world problems.  All of this would have normally been taught in the first month of Algebra 1 in 9th grade to the average student and now we expect 6th graders to do it!  Some just are not ready for this yet and we are doing a disservice by pushing it on those who are not yet ready, while at the same time our county will sometimes not allow advanced students to work ahead because they don’t want kids getting too far ahead!

To summarize, many students are going to struggle in Common Core Math 2 – it has very advanced topics that some students will not be ready to handle in the 10th grade.  Additionally, with block scheduling, students are expected to learn all of this advanced material at twice the pace since they have to learn it all in one semester rather than in a full year.

Written by:

Lynne Gregorio

Ph.D. Mathematics Education