Amidst all those factors, I always send peeps to Paul Lockhart's " A Mathemetician's Lament," which can inspire even the most jaded mathphobe - you can read it on the link provided or buy the book. It's a short, yet powerful read.
This particular post by Lynne Diligent addresses many of these topics from her perspective as a tutor. Diligent is an American expat teacher who has worked in International Schools in America, and an American School in the Middle East. As usual, let us know your riffs on this - Be sure to also check out Diligent's Part 2 -
- C.J. Westerberg
Why So Many Students Aren't Mastering Basic Math Facts
The Four Trends
by Lynne Diligent
A friend of mine teaches remedial math at the Community College level. We were discussing the problem of a number of students who never seem to have their addition facts mastered (much less their multiplication facts).
"I remember as a young math teacher wondering how many hours of flash card drill it takes in the elementary grades to become fluent in the addition and multiplication facts. I could imagine ten minutes a day of actual flash card drill, five days a week, for 45 weeks in one grade, a total of 50 hours if I multiplied correctly, might be a reasonable guess. Surely it has been studied. Well, if it has been studied I have never seen any evidence of it in the last fifty years. I thought of that as probably pretty basic knowledge about the teaching of arithmetic."
I'd estimate that at least 30 hours of drill, spread over a period of time would be required for an average child to learn addition facts, and an equal amount of time later on to learn multiplication facts. But there is NO classroom time provided for this in the math curriculum.
The problem here, speaking as a third-grade teacher of 8-and-9-year-old students for a decade, is that the elementary math curriculum (in America) is not structured to provide ANY time for drill such as he describes. Even when I was a child in the early 1960's, we did not have drill of that type in elementary school. My mother worked on flash cards with me 10-15 minutes every day before I was allowed to play. I HATED every moment of it, but saw the value of it when I got into the working world in my 20's and was using multiplication every day, knowing my multiplication tables by heart thanks to her efforts.
I've been discussing math teaching with other math teachers for several years now, and I find there are several trends I highly disagree with:
Trend 1: The amount of math homework has been cut in half from 24-30 problems nightly, to 12-15. I can only guess that this has come about from parents complaining about too much homework over the years. While I am in favor of not giving more homework than necessary, unfortunately, the current lighter homework often does not give sufficient practice in a certain type of problem for the students to be able to understand or master that type of problem. One or two examples of a certain type of problem are just not sufficient.
First Worksheet Below: Houghton Mifflin Grade 3 Math Homework PRIOR to 2007.
Second Worksheet Below: Houghton Mifflin NEW Amount of Grade 3 math homework, starting in 2007 (taken from end of a Grade 2 workbook)
Below: Houghton Mifflin NEW Amount of Grade 3 math homework, starting in 2007 (taken from end of a Grade 2 workbook).
Trend 2: Drill practice is considered "old-fashioned." Never mind that the teacher can make drill practice into a fun lesson, just like any other type of lesson can be made fun by a dedicated teacher. Without any drill, and without parents practicing or drilling children at home (such as the type of flash card practice my mother did with me as a child), many children are just NEVER mastering even the basic addition facts, let alone multiplication facts.
I no longer teach Grade 3 - I am now a private tutor. Unfortunately, I am now running across a number of 14-year-olds who are using calculators to add 5 + 3, or 7 + 6, or 9 + 2. What's even worse, THEIR TEACHERS LET THEM!!!! I personally think calculators should
just be thrown out until about Grade 11, or whenever math involving higher functions on calculators is started. Prior to that time, they shouldn't be allowed in school at all.
When I taught Grade 3, I made students show all of their work on their homework, including every carry number, and every cross-out for borrowing; I didn't allow them to say, "I did it in my head." (See photo above of example homework prior to 2007.) One reason for making students show all of their work (I had several reasons) is that I knew perfectly well many of them had calculators at home. However, even if they did their homework with calculators, they would have to redo it to mark all the carry numbers and borrowing cross-outs. This makes it better to just do it by hand in the first place. I then spent 30 minutes of my teaching time DAILY, going over these homework problems. It's so satisfying to a teacher to hear, "Oh! Now I see my mistake!" It's a big mistake for a teacher just to mark answers right or wrong, as students learn nothing from that.
Trend 3 (mostly at the high school level, I haven't yet seen it appearing in middle schools, although I could be mistaken): Don't instruct and explain, and then follow up with practice to master the skills. Instead, put students into groups, and let them see if they can "figure out themselves" how to do problems. Don't give much feedback, but of course, students will have the same test as if you taught them the traditional way. (So the parents who can afford it get math tutors to do at home the job that the teacher should be doing; the parents who cannot afford tutors or understand the math themselves have children who completely
Trend 4 (has been around for at least 25 years): It doesn't matter if children don't master
a unit. Just move through all the units, and the same units will be covered next year in
a little more detail. If they still don't get it, the same thing will happen the following year, and hopefully they will get it then. This idea has a name, which is called something like "spiraling."
Even though I've never seen it, in the past couple of years I've become aware that "Singapore math" requires mastery of each math subject to a certain degree before moving on to the next math subject. (Editor's Note: see The Daily Riff's exclusive series, "Singapore Math Demystified!" and additional links below).
I think students would be far better served by having HALF the number of math topics (eliminating topics in Grade 2 such as Data, Graphing and Probability; Congruent Shapes and Symmetry; etc.) and making sure they have mastered basic addition facts (by heart), addition and subtraction of two-digit numbers, and multiplication tables up to 5 (by heart) before moving into Grade 3. If parents don't have time to drill children at home on these facts, then some time for it should be allowed in the school curriculum. (cont. Part Two . . . )
You can find Lynne Diligent at her blog, Dilemmas of an Expat Tutor, where this post first appeared (with minor edits and additional links provided). We recommend visiting this link to read the lively and passionate comments in response to the post.
H/T to Joanne Jacobs: Why Math Tutors Prosper
Why Other Countries Do Better in Math: Should Parents 'Race to the Tutor?' (It's not what you think)
Why Our Kids Don't Get Math
Would you Hire your Own Kids? 7 Skills Schools Should be Teaching Them by Tony Wagner
Fires in the Mind: What Does it Take to Get Really Good at Something?
Part 1: Singapore Math -- Demystified!
Part 2: Can Solving Problems Unravel Our Fear Of Math?
The Singapore Math Program philosophy - Problem-based, concrete-pictorial- abstract approach
Part 3: Singapore Math: Is this the most Visual Math? The Signature Bar Modeling Method
Beyond Singapore Math: Resisting Quick Fixes