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November 2, 2009

Loyola professor sounds off on teaching math

On the paper's editorial pages today is a column by Loyola University's Joseph Ganem about the teaching of math.

He argues that some students are being taught overly complex math at too young an age. It is an interesting piece to read, although some commentors have suggested that perhaps his premise is wrong. Are we really teaching difficult concepts too early because of tests?

I wonder if that is correct because last week we wrote that the Maryland School Assessments for fourth-graders are some of the easiest in the nation.

What do math teachers think of Ganem's argument?


Posted by Liz Bowie at 1:57 PM | | Comments (8)
Categories: Around the Region


"He argues that some students are being taught overly complex math at too young an age."

He argues against overly complex math being taught at all (in many instances) but worst of all being done so in preference to first achieving both mastery and contextual understanding with lower level math (and even arithmetic) beforehand. The grade levels for where these events occur are incidental to his arguments.

And he is 100% correct.

I am also agree with Joseph Ganem. Every child has different capability to learn and grasp, so how we can decide an uniform syllabus for a term for all the students. Really a serious topic to be given a thought.

The problem with standardized tests is there is always about 800 opinions about the "difficulty".

Maryland at the same time: Is the best school system in the country, has the easiest fourth grade tests, is one of only 25 states that ties an exit test to graduation (thus being more rigorous than half the country), etc etc etc.

I have been reading and hearing a lot of papers (and lectures) recently that we need to re-think the way math is taught in schools. Moving away from Calculus being the overall goal with more of a focus on advanced statistics and theory.

There are good arguments for each. I am a Government teacher myself, so I really can't speak on the matter. But I do see examples in my field that students seem to be rushed into higher-level maths and sciences at the expense of mastry of basics.

What this results in is a student's knowledge base is 100 yards wide, but only six inches deep.

In Howard County, the lack of early preparation for higher level classes has been increasingly apparent for the past 30 years. The math textbooks have become more "colorful" but lack the continuity and rigor of earlier texts (I fondly remember the Dolciani Algebra series). There are high school students who have not memorized their basic facts and can't seem to compute without a calculator in their hands. Administrators are asking teachers to "differentiate" and use more games in their instruction so that the children are not "bored". What used to be a rigorous final exam has now become the very easy state HSA which any prealgebra student could pass. There are students who are waived into courses without the necessary prerequisite skills simply because their parents don't want them in the "regular" levels - those students require extra attention and ask so many questions that they hold up the class. Years ago, one required a math degree in order to teach math, now they only have to pass one Praxis exam and they are magically a math teacher! All I can say is "I'm glad my children are no longer in the school system". If there are so many problems at the high school level, why is it any surprise that students are going to college unprepared?

The goal for teaching math to Maryland students should focus on developing a relational understanding of concepts. On one hand, this piece criticizes educators for their focus on raising basic [grade level] standardized test scores, while at the same time making generalizations about math instruction in MD, based partially on the isolated experiences with difficult or rigorous mathematics problem(s) encountered in a homework assignment.

The issues mentioned seem more directly related to instruction than curriculum, state standards or state testing. MD curriculum standards are the floor for instruction and the ceiling for [state-mandated] assessment. MD Educators strive to help students master the State Curriculum standards; and yes, they often challenge students to develop a deeper understanding of some topics beyond these grade level standards. Although certain portions of the MD assessments are rigorous, items reflect course/grade level expectations, and therefore do not test topics that extend beyond state assessment limits.

The MD Algebra/Data Analysis State Curriculum requires that students apply formulas and/or use matrices (arrays of numbers) to solve real-world problems. However, it is clearly stated that inverse and determinants of matrices are not assessed at the state level.

The thing that strikes me the most is when the discussion of process vs. understanding. And it is led by the assessments. We no longer teach Algebra 1. We now teach a ‘watered-down’ pre-algebra curriculum that caters to the test, not the skills that students need to move on. The testing is dictating what is going on in the classrooms. Rote memorization is a thing of the past. Technology can do the processes (ie: spreadsheets, calculators, math programs, etc.). But students have no understanding of the “output” from these processes, which leaves them with no number sense. That is most of what makes them ill-prepared. That is what is lost. Instead of making sure students have an understanding of the basics in the early years, we focus on calculators and technology; students never develop a number sense. What effect does that have on our students? If a student puts a multiplication problem into the calculator (say 23 * 25) and the calculator gives an answer of 50 (just an example), the student will write 50. They know the process but do not understand enough about numbers to know that 50 is an impossibility. They obviously put something in wrong while using the calculator but can not recognize their errors. And this does start because we are putting calculators and other technologies in students’ hands to increase ‘rigor.’ Students are expected to do more than they are capable of. I could go on and on and on. It is interesting to hear College Professors say the things that high school teachers are saying. The disconnect REALLY is with the policy makers and decision makers. We all KNOW what it takes to be successful in college and beyond!

P.S. Don’t even get me started about the middle school curriculum!! I could talk all night about how bad that is!!!!!!!!!

The Howard County texts are inaccurate and since the nation only uses 5 publishers for all texts, it's safe to use inductive reasoning here.

We're falling behind the rest of the world and it's our own doing. Remove the politics from education and skill will have room to breathe.

@virgilfordante -

"Remove the politics from education" - you're kidding, right? What in the world is more political than education? We've got public education which is obviously funded by politicians with poor districts vying for fair funding vs. rich districts with a political formula that is used to decide funding. You've got the wealthy and those who aspire to raising their standing in the class structure opting out of a failing public education for an expensive private education. Is there anything more political than class structure? You've got parents and their tax dollars moving to districts with "good schools" and abandoning districts with "bad schools. You've got NIMBY attitudes about schools and students from neighbors who are victimized by crime (or a perception of crime in some cases) radiating from schools. You've got astonishing disparities in school buildings, technology, social service needs etc between schools and between school districts. Oh, and don't forget that you've got the future elections being decided by the kids that are now in school (at least those who are not so disillusioned with the political system that they don't vote or turn to crime and can't vote).

Don't tell me you're so naive that you think there's no connection between tests and curriculums and funding and politics. Remove politics from education? You must be living on a different planet then the one I (and my 3 kids currently in school) live on.

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