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Tutoring Common Core Mathematics 2 – the struggles for students

17 Oct

I am an educator of 25 years and have a Ph.D.  in Mathematics Education.  If you read my blog, I have been vocal about my dislike for the New Common Core curriculum.  It is very choppy and does not help students build a big picture of mathematics as they skip around from one unit to another.  For those unfamiliar with the changes to Common Core Mathematics, many of the standards from Algebra 1, Geometry, and Algebra 2 – including topics in applications of Statistics, were broken down into pieces or individual units.  Next, the creators of the curriculum went through and picked topics from across all 3 old math courses and divided them up differently into Common Core Math 1, 2, and 3.  They added a lot more verbage that describe the individual units and how they can be learned at a more conceptual level and then tried to link as many pieces as they could to mathematical modeling.

Did you ever wonder why our system used to go from Algebra 1 to Geometry and then to Algebra 2?  Why not do Algebra 1, Algebra 2, and then Geometry?  Well, a school in our district wondered the same thing, the idea was that students would forget less Algebra if they did Algebra 1 and 2 back to back and then do Geometry afterwards.  However, when they tried it, they found out the reason (probably what people found out long ago and the reason it has always been done in the old order) why students in high school do best with the order Algebra 1, Geometry, Algebra 2.  The reason is that students need time to mature into mathematics.  The higher level of mathematical thinking required in Algebra 2 was too high for many students to be successful in their sophomore year (the typical age for the average US student to take their second math course).  Geometry is much easier and gives students the chance to grow and develop before they are presented with the harder mathematical concepts learned in Algebra 2.  The school in our district did this for one year and then after finding that it was not successful, went back to the old order.

So, why do I bring that up?  Well, in Common Core 2, students are back to doing many Algebra 2 topics again in their second year of high school mathematics and we are seeing the same problem as we did when we tried to get students to take Algebra 2 in their sophomore year.  The students are not mathematically developed enough to be able process those Algebra 2 concepts.  I am currently working with some students in Common Core 2 and I want to discuss their struggles.

Common Core 2 in our district is taught in one semester on block scheduling.  This means 90 minute classes for one half of the year = an entire years class that another school might offer without block scheduling.  Therefore, the math material moves twice as fast and students can go as long as a full year between math classes.  For example, they have a class Fall Sophomore year but not again until Spring Junior Year.  Although I was given the “standards”, it was very hard to interpret what the school was actually going to do with it.  Our schools don’t use books.  My son’s school (he is taking Common Core 2 at a middle school – and therefore will have a full year since they don’t do block scheduling) have been using a an applied curriculum with outside resources that looks nothing like what the high schools (both being under the same state standards) are doing.  Other middle schools in the state have been bringing in topics that the high school students will never see since they also are not on block scheduling and it gives them much more time than the high schools.  For example, one middle school covered partitioning line segments but the high schools do not cover that.

Common Core 2 in high school has had almost no Geometry so far.  Their first unit covered dilation, translations, reflections, and rotations and during the second unit they very briefly talked about proving triangles congruent and similar.  The majority of the course has been spent on topics they did in Common Core 1, topics one would see in Algebra 2, or expanding on functions they learned about in Common Core 1.  For example, even though they fully covered how to translate, reflect, and stretch parabolas in Common Core 1 they did this again.  They are also doing it AGAIN with exponential functions.  Even though students learned how to graph quadratics in Common Core 1, they had a huge unit on graphing quadratics, finding zeros, factoring, using the quadratic formula, and finding the discriminant.  Students also learned how simply expressions with exponents including negative exponents in CCM1 yet it is repeated in CCM2.  Students learned how to simplify square roots with variables and now in CCM2, they expand it to simplifying with high roots.  They also expand by adding rational exponents and solving equations with square roots and rational exponents (an Algebra 2 topic).  Later in this unit, they will review exponential functions and look at the idea of how to write recursive functions (recursive functions are usually taught in Algebra 2 or Advanced Functions and Modeling which comes after Algebra 2).  So far, the course has had almost no resemblance to a traditional Geometry class, so it makes me ask if students are going to get any traditional Geometry teaching anymore?  I did read that “proofs” are supposed to be included in CCM3 so I wonder if CCM3 will be Geometry heavy.

Now that I have addressed the content of the course, I want to talk about student success.  I work with students who are trying to learn the material in CCM2.  The current unit with rational exponents is moving at a fast pace and requires that students have a true understanding of the “rules of mathematics” in order to be successful.  Math must be done in a specific order.  When solving a radical equation, especially one that will generate 2 answers, there are so many steps involved that any struggling student will get lost in all the steps and rules.  Unless you intuitively “get” math, these rules and required order won’t make sense.  Many kids try to memorize the steps and at a fast pace with so many rules and changes that happen from problem to problem, memorization fails.  Either you naturally understand why you are doing each step or you just can’t get there.  For so many kids, they just can’t or don’t get to that step.  Their brains are just not wired that way.  I think about it this way, I can’t whistle.  It isn’t hard for someone who can do it, they just can.  However, even though I try and try and I follow the directions everyone gives me about what to do, I am just not physically capable of whistling!  Math teachers are people who can whistle and the problem is that they don’t understand people who cannot since their brains just “get it.”  For some kids, it is a matter of not trying, not applying themselves, etc.  I see that a lot.  I also see that our curriculum and pacing is NOT helping students get where we want them to but when we have students who have brains that are just trying to memorize math as a bunch or random rules rather than seeing the big picture, we have to accommodate that by a) creating a curriculum that allows to gradually live up to the potential they are born with and b) move at a pace that gives them the time to figure out that picture.

At the current pace and with the current scope and sequence, we are just asking for failure among many students.  I leave you with this?  If our goal is to get from level 1 to 10 with students by year 12.  What is better, going slower and actually getting to 7 by year 12 or going fast and pushing to level 10 with lessons but the student is really only at a level 4 since we lost them long ago!

 
 

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