I have stated this before in my blogs but after receiving a funny video and having yet again more situations fall in my lap that just get my blood boiling about Common Core, I thought I would revisit this idea with another short blog. Let’s start with this video reminding us about New Math.

For those not familiar with New Math, it was a movement of moving away from application, basic skills practice in favor of developing a deep conceptual understanding of the content. The process became more important than the answer and providing these abstractions to children who were not ready for this and by not providing the correct amount of practice of basic skills, we lost a generation of people who neverlearned math and feel it is just a confusing mess.

“….Some of the New Math curricula were excessively formal, with little attention to basic skills or to applications of mathematics. Programs that included treatments of number bases other than base ten, as well as relatively heavy emphases on set theory, or more exotic topics, tended to confuse and alienate even the most sympathetic parents of school children. There were instances in which abstractness for its own sake was overemphasized to the point of absurdity.^{37} Many teachers were not well equipped to deal with the demanding content of the New Math curricula.” (http://www.csun.edu/~vcmth00m/AHistory.html)

So, why do I feel that Common Core is the same as New Math? Well, I can only speak for the standards and the methods that my wonderful state of North Carolina is handing out but I see an eerie similarity. It is especially noticeable at the high school level. It seems that this “Integrated” approach to mathematics seems to be the new “hot” item over the traditional Algebra 1, Geometry, Algebra 2 sequence. Why? I asked this question. The answer was to better link concepts that relate to each other. Hmmm… wouldn’t Algebra 1 topics best relate to topics within Algebra 1 and Geometric topics best relate to topics in Geometry? Just seems like we already had a good system of linking similar topics. So, moving away from that, the second reason is to provide a “Commoness” so that all states are doing the same thing. All schools are producing students with this same deep understanding after Common Core 1, 2, and 3. However, since some states and even individual schools did not choose to adopt these standards, we now have students taking: Integrated Math 1,2, 3 (Common Core Style) or Algebra 1, Geometry, Algebra 2 (Still common core style), or Algebra 1, Geometry, Algebra 2 (NOT common core style). So, what about the student who takes Common Core Math 1 and 2 at one school and learns just a little bit of Geometry in those two classes but MOST of the Geometry is withheld until Common Core 3, now that student moves onto a different school (this is common for some middle schoolers and my son may be a victim of this) and the new school doesn’t do Common Core Integrated Math but one of the other two options. Now, he has missed most of Geometry and is taking Algebra 2 (either Common Core style or not). He takes his SAT and they ask him about finding the area of a segment of a circle. Well, that was done in Common Core 3 but he didn’t take that because his new school wasn’t doing the same path, he is out of luck or gets to learn all those missed concepts on his own before the SAT.

Thirdly, we haven’t yet discussed the fact that teachers are still trying to teach at this higher conceptual level with less traditional drill and practice of standard Algebraic and Geometric problems. This is exactly what happened in New Math and we lost many students who just couldn’t grasp the concepts well enough at that higher level and without the standard drill and practice of working with exponents and solving geometric problems with parallel lines, now don’t possess those skills either. This isn’t jut me “theorizing” it could happen. I saw it happen last year as one school tried to teach with all investigations and a very limited amount of standard algebraic drill and practice and these students are now very weak algebra students.

My son is working from a new “investigation approach” for Common Core 2. After going to the website to read about it, they boast how their students scored above (in one area) or the same as (in another area) other students who took a traditional 1 year Algebra class after their test students took 2 years of their Common Core sequence. This left me scratching my head? How can you compare two groups where one group had 1 year of instruction and the other had 2 years of instruction? Note my comments are in blue.

“…on the Educational Testing Service’s *Algebra End-of-Course Examination*, students at the **end of Course 2 [at the end of this second course]** scored especially wel**l**on subtests of Concepts and Processes **and about the same** on Skills **as a national sample of students who were completing a first-year algebra course**. **[this other group was just completing their first year of a traditional algebra class, did they score especially well too? didn’t say]** For further discussion of the *Algebra End-of-Course Examination* findings.” (http://www.wmich.edu/cpmp/longitudinalstudysummary.html)

When I looked at the “further findings,” the study was never clear that it was equating students with the same number and level of math experience when comparisons were made. It also said that the students who took the “Investigation” based class scored better on those types of problems but worse on basic skill type problems than those in a regular curriculum. This makes obvious sense since the focus is much more applied in the “Investigation” based approach and most Algebra teachers (although this should not be the case) don’t always do enough applied problems with students although they cover the manipulations well. When looking at SAT and ACT scores, the Investigation group did better on SAT and the traditional group did better on ACT mathematics. With the back and forth of who was better and the lack of comparison of the same exact preparation in all cases, I don’t believe you can call this study a reliable study that in anyway shows that this “Investigation” approach provides benefit to our students.

The bottom line is that students need BOTH. We seem to always be at one end of the spectrum or the other. They need both conceptual understanding and procedural practice to be successful. Every student is also different, some students will be more successful with procedural math and really have a hard time “seeing” conceptual mathematics, other students might be bored with procedural math and really be able to grasp math in a very advanced, creative way with good applications, a small amount of theory and concepts presented (these will likely be your future math majors!).

To speak for myself, I fell in love with mathematics because of Procedural Algebra. I LOVED to manipulate algebraic equations and later Calculus derivatives and integrals. The concepts grew for me over time but without my love for procedural mathematics, I would never have pursued higher degrees in math.

Written by: Lynne Gregorio

Ph.D. Mathematics Education with minor in Statistics (since I loved statistical manipulation)

M.S. Mathematics with minor in Secondary Education

B.S. Mathematics with minor in Philosophy and Secondary Education