Why So Many Elementary Students Aren’t Mastering Basic Math Facts
Re posted here with permission.
“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.
|Houghton Mifflin Grade 3 Math Homework prior to 2007|
|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 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.
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 fail math).
|High school math class, with students working in groups.|
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.
Some important topics, which are covered briefly in the curriculum, but to which little or no time is devoted to practice or mastery of these important life skills: making change for customers, knowing addition and multiplication tables by heart, knowing how to do the simplest operations without a calculator, being able to recognize a wrong answer when a wrong button has been pushed on a calculator, developing estimation skills, becoming competent in measurement and fractions (useful to every housewife in halving or doubling recipes on a daily basis).
Consider: Are we not cooking anymore in American society? Are we not hanging picture frames? Are we not doing any home repairs or improvements ourselves? Is there never a need to count back change? Does no one sew or do woodworking for pleasure anymore?
Here are five examples of the types of things I feel should be eliminated from the Grade 2 curriculum (for seven-year-old students):
|Grade 2 spending time learning to differentiate between types of quadrilaterals.|
|Grade 2 spends time working on composition of shapes viewed in 3D.|
|Grade 2 spends time learning about congruent shapes.|
|Grade 2 spends time on learning about lines of symmetry.|
|Grade 2 learns about slides, flips, and turns of geometrical figures.|
In my opinion, more time needs to be spent on mastery of basic life skills in the early elementary grades.
One last point about the spiral curriculum. Math educator Brian Rude feels that the spiral curriculum should not be thrown out entirely, but that the problems are caused from barely touching on subjects each time, instead of cutting a bit deeper, so that information is retained. He points out, however, that if cuts are too deep, that there is a danger of never having time to return to that subject, and students will also forget. He feels a balance between the two extremes is best.
Singapore Mathematics Curriculum: An Example of Spiral Approach
"Singapore mathematics curriculum emphasizes the spiral approach based on Jerome Bruner's explanation on spiral curriculum. The idea of the spiral curriculum, according to Bruner - 'A curriculum as it develops should revisit this basic ideas repeatedly, building upon them until the student has grasped the full formal apparatus that goes with them.' Most people will not miss the idea of 'repeatedly' but may miss the subtle notion of 'building upon them' and 'until the student has grasped the full formal apparatus' of the target concept. In Singapore curriculum, addition is taught four times in Grade 1 (this is a core idea and they are new to it) - addition within 10, within 20, within 40 and within 100. Students get to revisit the idea of addition repeatedly but each time building on the strategies that they already had. When they add with 10, they count all and count on, perhaps with the use of concrete objects and drawings. Later, in addition within 20, they learn to make ten before adding, effectively acquiring the notion of place value. Later they progress to more formal approaches such as adding ones and adding tens in the formal algorithm. Thus, it is not mere a review of materials. It involves extension. In a similar way, multiplication of whole numbers is taught in grades one through four; addition and subtraction of fractions is taught in grades two through five; area of plane figures is taught in grades three through seven; solving equations is taught in grades seven through nine. As a result, in Singapore, Algebra is taught across grade levels in high school (grades seven through twelve). Thus, we do not have the practice of teaching Algebra, Geometry etc separately. They are all under the subject of mathematics. There is geometry in all grade levels."