Posts Tagged ‘integrated 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


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.