Comments From University Professors On Integrated Math vs. Traditional Math

Professors were contacted via email from the following Universities and were asked their opinion of traditional math vs "Integrated Math": Washington University, University of Missouri, University of Wisconsin, University of Minnesota, Indiana University

I want to give you a short answer to your concerns:
Stick with traditional Math.

Here is a site that I developed for the University of Missouri. The URL is http://mathonline.missouri.edu Students who score above 75% on a specific test (Algebra, Geometry, Trigonometry, Calculus readiness), would be judged as proficient in this subject. I do not think that the majority of the students taking IM will score well on these tests. Get you children to practice often on this site before they take the ACT or SAT.
~Professor Elias Saab, University of Missouri

From my experience of teaching mathematics at the college level for fifteen years here in Missouri and in Texas and also from my experience as a parent of two children who went through this whole system, I think that middle school mathematics as it is now, traditional or Integrated, is a complete waste of time. Integrated mathematics is even worse because it eliminates the last traces of logic in mathematics and leaves the students lost and unprepared for college. Without introducing algebra in middle school things will get worse every year.
It is very visible how the level of math preparation goes down, with students unable to apply elementary mathematical procedures. This decline became faster after introducing Integrated Math and similar innovations. Please see below my statement in response to a request similar to yours. You can use this statement in any way you wish. I think that the state of the secondary math education in the US is a disaster of enormous magnitude that will affect the development of the country for many years.

On the state of middle school math education in the US.
The quality of the secondary math education in the United States has long become a standard joke among mathematicians around the world. It is very painful to see how the most powerful country trails behind European, Asian and third world countries in the level of mathematical skills of high school graduates. This concern has surfaced in the most recent State of the Union address, so it is clearly getting the national attention.
To my opinion, the major reason is that, unlike many countries, algebra is not included in the middle school curriculum in the United States. Algebra was invented a few thousands years ago as the universal language of mathematics, allowing to avoid lengthy word explanations of mathematical procedures and making mathematical studies logical and connected. It is essential that the students start learning algebra as early as in the 5th grade, which brings mathematical formulas to them naturally later in their lives. It is still possible for the best students to start algebra in the 8th grade and be successful, but in general American students continue looking at mathematics as a foreign language. I think the switch to starting algebra in the 5th grade must be made as soon as possible, by adopting a system used in one of the countries like Russia, France or Germany. American students are as smart as anybody, and they and their teachers will quickly adjust to this system.
The so-called Connected Mathematics Project, Integrated Math and other recent innovations are even worse than the "traditional" American system. They further water down the curriculum and leave the students largely unprepared for college mathematics. Instead of bringing our children back to the level of "ancient Greeks playing with stones on the beach", American math education must quickly switch to the most advanced methods of mathematical learning.
Sincerely,
Alexander Koldobsky
Leonard M. Blumenthal Distinguished Professor of Mathematics
University of Missouri-Columbia

At present, I am not aware of any rigorous comparative studies contrasting the performance, in college math courses, of students enrolled in integrated vs. "traditional" math curricula in high school. The integrated curriculum has not been in place very long, at least here in the state of Missouri, and most of our current students at MU have come from a traditional background. In the next few years, we may begin to see the effects of the integrated curriculum. However, I have looked at the integrated curriculum as practiced here in the Columbia public schools (and my impression is that the integrated curriculum here is similar to that in other districts), and I believe that the traditional curriculum is clearly preferable. I expect that, eventually, we will see that students who have studied the traditional curriculum are better prepared for university level math courses.
I first became aware of "integrated math" around 4 years ago, when my son, who is now in his junior year in high school, was preparing to enter 8th grade. At that time, the Columbia Public Schools had just begun the transition to an integrated math curriculum, but 7th graders who had scored highly enough on a certain standardized national mathematics test were granted the option to choose to follow the traditional curriculum, beginning with Algebra (normally considered a 9th grade course) in 8th grade. All others were shunted into integrated math. Fortunately, my son was among those who qualified for the traditional option, which we did in fact choose, after first attending a presentation on integrated math, and after I had examined the textbooks for the integrated course. As an 11th grader, my son is now enrolled in traditional Pre-Calculus, and I still have no doubts that choosing the traditional curriculum was the right decision.
Let me explain my point of view on this business. The true essence of mathematical reasoning is the ability to recognize and to exploit patterns and structure, to reason from an abstract principal, to recognize that some concrete example is a particular case of a general phenomenon. In some sense this is reasoning in its purest form. Developing this sort of reasoning ability is (or should be) the central aspect of mathematics education, an aspect far more important and useful than emphasizing "real world" applications. It's not that those applications are not important - of course they are. It's just that students who have really learned to reason mathematically can easily master the skills involved in applications. It's the difference between learning to think vs. just learning some practical methods. If you first learn to think, methods are easy. My considered impression of the integrated math curriculum is that the emphasis is on learning mathematics only to the extent that it is a tool for use in practical applications, as opposed to learning to reason and to recognize abstract structure. I would therefore caution against the abandonment of the traditional math curriculum.
Steve Hoffman, Mathematics Professor, University of Missouri

Your letter raises an interesting point: I don't know whether anyone has tracked how student do at college as a function of which math sequence they have had in high school.
I don't want to comment on one of the sequences in Clayton over the other without knowing exactly what is covered in each. However:
You are right to be concerned. College-bound students should certainly be exposed to the most comprehensive and rigorous program possible ("possible" taking into account the individual student's abilities), particularly if they want to have any realistic chance of doing well in a field requiring mathematics. There is no way to make up in college for inadequate K12 preparation. I see too many students whose real potentials we will never know, because, intelligent as they are, there are simply too many gaps in their skills for them to do well in a college course.
~A Mathematics Professor who preferred to remain anonymous, University of Missouri

The following is mainly my opinion as the research is quite mixed on this topic. To give you my background, I am a mathematician who also has doctoral coursework in educational psychology, gifted education, and psychometrics (the theory of educational testing). First, I believe that the overall concept of integrated math is a good one, but to be effective, it takes phenomenal teachers and a more balanced approached (mixed with a traditional approach) than most school trials as using. There are two aspects of mathematics that are important, and it is critical to address both. The first aspect is computational and algebraic fluency. In the same way that language fluency requires study and not just practice, mathematical fluency also requires practicing correct things. While it is vitally important that students understand "why" they are doing things, the first step is getting them to do those actions correctly. The problem with "discovering" mathematics is that many student discover incorrect concepts and they are almost impossible to unlearn. Again, with a great teacher, these concepts can be taught correctly, but the sad fact is that only 5% of teachers in junior highs and high schools are even close enough in their own understanding of mathematics to be able to teach the material in an integrated fashion. I personally would say that my own teaching style is quite integrated, but even in a college environment, only the very best professors are able to use this approach successfully and when I have students who come in with an already weak background, this approach actually results in lower test scores.
If you are interested in test scores, the traditional approach wins hands down. Asian schools teach extremely traditionally and with great success. My foreign students usually are two levels above their American counterparts in their ability to manipulate functions and do algebra. At the same time, foreign students come to US colleges and universities because we teach students to think critically and be creative, something which is extremely hard to measure on a test, but is the critical advantage of integrating math.
So to summarize, students really need to know basics before they can go on to higher levels of thinking, and from take on the research, most integrated math curriculae fail to sufficiently teach the basics or even allow students to learn incorrect methods. I do think it is important to apply and understand math and that our traditional approach focuses much to much on rote memorization. Having taught almost 5000 freshman in my career, I would prefer having a student with solid basics (even if they are memorized) over a student who is creative but doesn't have these basic skills, so I would recommend the traditional approach unless you know the integrated approach has a better teacher. As a parent, the choice of teacher is much more important than the choice of curriculum, but if you can't chose your teacher directly, I strongly recommend a traditional curriculum.
Jeremy Boggess, Mathematics Professor Indiana University

I have no experience of the "integrated math" curriculum, so I cannot competently answer your question. From my experience with other "reformed" or "innovative" programs, I have learned to be rather skeptical. Mathematics has been taught for over 2000 years, and many good methods have been discovered during that time. New programs tend to ignore that vast experience in favor of untested methods. Thus, as a matter of principle, I would favor the traditional curriculum.
I confess to being rather ignorant about the Core-Plus program; nevertheless, I do have some negative thoughts about it. There is a rather good evaluation of how students perform at Michigan State University: "A Study of Core-Plus Students Attending MSU," by R. Hill and T. Parker. You can find this article under the web address: www.math.msu.edu/~hill/HillParker5.pdf
~ A Mathematics Professor from Washington University

I don't know much about Core-Plus. In fact, until receiving your note and conversing today with Richard Askey, I'm obliged to confess I hadn't heard anything about it. However, my brief conversation with Professor Askey left me horrified. The approach followed by Core-Plus strikes me as a very poor preparation for college-level mathematics courses. Were my children asked to choose between the Core-Plus program and a traditional mathematics program, I would urge them to select the traditional program.
~A Mathematics Professor from Washington University

In particular, I'm unable to guess a rationale for putting the brightest students in a Core Plus program. These are exactly the students who could be expected to benefit most from a traditional program.
~A Mathematics Professor from Washington University

There is a very good study done at Michigan State University you should look at, the results are pretty clear: http://www.math.msu.edu/~parker/monthly905-921.pdf (There are competing studies, one from Washington state, but I wouldn't trust that one...) Our department also has a list of problems we expect our incoming science/engineering oriented freshmen to be able to handle: http://www.math.wisc.edu/~maribeff/problems.pdf. These problems are typically handled better by students from traditional math backgrounds. Please let me know if I can be of any further help.
~Professor Steffen Lempp, University of Wisconsin

I am not certain that I have the vocabulary correct, but I feel that traditional math (emphasizing technical skills, as well as understanding of concepts) is highly preferable to the often popular emphasis on "real life" word problems and group activities.
~A Mathematics Professor, University of Minnesota

`Integrated' is an adjective. Whether it applies in a particular situation can be a matter of judgment. There are various textbook series that self-advertise themselves as `integrated math'. For some, my own view is that a more accurate adjective would be `fragmented'.
And there is also the issue of `integrated' in what sense. I am very much in favor of integrating aspects of geometry with both arithmetic in earlier grades and algebra at higher grades. But it seems that the current commonly used phrase 'integrated math' means `integrating with applications' and, in the worst cases, jumping around among math topics to fit the applications. `Integrating with applications' sounds good, but often in the attempt to make the applications real-worldish, many text pages (and I would think much class time) is taken up with non-math descriptions in situations where the math itself is not sufficiently substantial to warrant that attention.
Actually, `integrated math' often seems to be more about a certain view of pedagogy than about the mathematics itself. This would be fine were the appropriate math skills set as the fixed goal with there being differences of opinions as to how they should be attained. In practice my sense is that doctrinaire views about pedagogy tend to change the goals to fit the pedagogy---and in the particular case under discussion, to greatly deemphasize calculational skills as a desired goal. And at an antecdotal level I certainly see the effects of this deemphasis in my university classes.
But I think that in Minnesota we have turned the corner back towards an emphasis on skills combined with knowledge and understanding. I do not know if we have yet turned the corner on story problems to those where the emphasis is not on `interesting color' but on converting clear verbal descriptions into mathematics. In saying this I do not want to underestimate the value of `interesting color' as a motivational vehicle for students---although it is a tough one to use because different things motivate different students. For instance, arithmetic with baseball statistics could be a great motivator for some students, whereas for some other students it creates an extra level of learning---that, for instance, when one hits the ball it might not be called a hit and that when one is at bat and walks it is not called an `at bat', and, moreover, that it is OK to jog when one walks.
~Professor Bert Fristedt, University of Minnesota

My general impression is that students trained with CorePlus struggle much more with college math than other students. If you ask math profs, they will always want traditional math. However, in this case, I think there have been statistically significant differences in math ability levels with the Core Plus group.
~A Mathematics Professor, University of Wisconsin

There are no easy answers to your questions, because there are many integrated math programs and many traditional math programs, and much depends on how well the teachers are prepared to teach these programs. For example, I am well-acquainted with one high school that went from very low test scores to very high test scores by adopting an integrated math program and doing a lot of training of the teachers. But when those teachers retired and new teachers came in, the test scores dropped so much that the high school went back to a traditional program. Core Plus is a very popular integrated math program, but I think it is particularly difficult to use it to prepare students for college mathematics. This opinion is shared by many high school teachers that I know who are in favor of other integrated math programs.
Our experience generally with integrated math programs is that students from such programs are more likely to need remedial help in college. But as I said before, much depends on the implementation and how well the teachers are prepared. I would say that teachers who successfully use integrated math programs actually mix in a lot of traditional material, in order to help students get the algebra skills that they need. Integrated math programs tend to shortchange students in the algebra skills, and students who are weak in algebra have difficulties in college math. Integrated programs put extra emphasis on probability, statistics, and discrete math, which are not as important as algebra in preparing students for college math, particularly for calculus.
~Professor Lawrence Gray, University of Minnesota