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

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

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

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

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

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

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

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

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

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