Posts Tagged ‘north carolina math’

Quality over Quantity: A New idea for Math Education

08 Aug

“I can’t do Math,” you hear this said over and over by children and adults alike.  It is even “acceptable” to tout that “math isn’t your thing.  You don’t hear people saying, “I can’t read,” yet it is okay to almost brag that you can’t do mathematics.  Why is math such a hard subject for our country?  When and how does it fall apart?  As a math educator, I see so many solutions to our national math crisis that have just never been tried.  We always seem to just play around with the ideas of “the basics,” learning the concepts behind the mathematics (conceptual learning, new math, mathematical modeling), and procedural learning (very similar to the “basics” in many ways.)  All those things are important and we have a problem of tending to lean to one side vs. the other rather than keeping a reasonable balance between the two.  However, what I see as the biggest problem is looking at, “what is our ultimate goal?”  When I read an article that says a California College has done away with the requirement that all students must show mastery in Intermediate Algebra for college because non-STEM students don’t need math, it gets me thinking.


If non-STEM majors don’t need math, then do STEM majors no longer need to take literature classes and humanities classes required in the general education classes, these are not “needed” for their majors?  Why do undergraduate degrees require students to take general education classes in addition to their major focus?  We know the answer. It is the same reason why high schools require 4 English classes, 4 Math classes, 3-4 Science classes, 3-4 History classes, etc., in order to make a well rounded educated person.  Just like English, knowing math provides a level of competence for getting around in the world, it allows you to think critically, math is used in many places that kids don’t realize until they get to be an adult.  Adults who truly understand Intermediate Algebra, will be able to make more sound financial decisions in their own personal financial choices.


Additionally, Intermediate Algebra as a prerequisite for a college level math course, shouldn’t be too hard since Intermediate Algebra is a class that should be mastered in high school.  So, why is a high school math giving college students so much trouble that a college has to drop a high school remedial math class requirement?  This is because how we currently teach high school math is a failure.  Let’s face it, some students will struggle more with mathematical concepts and others will move on and take Calculus 3 before graduating high school.  There is nothing wrong with either student but we act like there is and we need to stop this.  We need to stop putting on kids on the same math trajectory and expecting it to work.  


My feeling is that the goal for graduation of high is to pass, with a B or better, Intermediate Algebra (which should replace tedious useless work with real world knowledge like understanding the Normal Distribution so you can talk intelligently about IQ scores and statistical research as well as linking concepts to real world like amortization tables for car loans and mortgages, these ideas are more important that long division of polynomials and adding rational fractions which is tedious.)  Students should be able to take the “slow path” to math if they need it where they learn the main topics in Algebra 1, some lighter topics in Algebra 2, and some of the basic ideas of Geometry (no geometric proofs).  The goal would be mastery of these topics at a B level.  Anyone graduating should be ready to prove their understanding to a college prerequisite test and be ready for a Pre-Calculus class, although, if they are not a STEM major, they may choose Statistics or Financial Math.  


Right now, in NC, we require students to take 4 years of math.  They start learning Algebra 1 concepts as early as middle school so that once in high school, they are already learning topics in Algebra 1, Geometry, and some starter Statistical topics.  By Math 2, they are being introduced to Trigonometry, Algebra 2, Probability, more Geometry, including proofs, and a small amount of what used to be in Pre-Calculus.  By Math 3, the students are finishing Algebra 2, finishing Geometry, taking on more topics from Pre-Calculus, and adding in more Statistical topics.  After Math 3, students must take a fourth math course.  Most non Honors students take Intro to College math, which ends up being a review of Algebra topics or Discrete Math, which goes into Probability, Statistics, and Decision Making.  If students were mastering all these topics, this would be wonderful but students are barely grasping all of this.  We need to slow it down and cut out the fourth class, cut stuff from Math 1-3, and although still require 4 full years (not semester blocks) of math for the non-Honors track but focus on QUALITY of instruction and MASTERY of learning, rather than QUANTITY of material we can “say” they were exposed to.  We will have students who learn more, are less stressed, and have a higher success rate in future math courses in college.


Students who are on the Honors track, can continue to be on their own schedule as they should not be slowed down.  They can meet that high school requirement while in middle school, take the “test” showing mastery and once they get to high school, they can be moving on to learning the missing pieces from Algebra 2, Geometry (with proofs), and move into modeling classes or Pre Calculus, Calculus, Statistics, and beyond.


Written by:

Lynne Gregorio, Ph.D. Mathematics Education


The Good and Bad of Common Core Mathematics

21 Dec

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

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

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

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

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

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

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

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

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

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

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

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

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


Lynne Gregorio, Ph.D. Mathematics Education


Learning Mathematics Through Achievement Learning Based Model

07 Apr

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

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

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

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

Bright students may have a schedule that looks like this:

Block scheduling:  (just a sample)

First Semester        Second Semester

CCM 1                            CCM2

CCM3                             Precalculus

Calc AB                         Calc BC

AP Stat                          CCM – helper



A slower student might look like this:

First Semester           Second Semester

CCM1                               CCM1

CCM1                               CCM2

CCM2                               CCM2

CCM2                               CCM3

CCM3                               CCM3


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

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

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

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

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


Written by:


Lynne Gregorio, Ph.D.


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

18 Jan

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

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

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

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

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

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

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


North Carolina Common Core Math 1 – what is it?

11 Dec

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!