Differentiated instruction is awesome.
At its best, it not only acknowledges that students are at different levels but also embraces the fact that they might learn material in different ways. As Tracey Hall, Nicole Strangman, and Anne Meyer point out, “The model of differentiated instruction requires teachers to be flexible in their approach to teaching and adjust the curriculum and presentation of information to learners rather than expecting students to modify themselves for the curriculum.”
There are dozens of great math games online that adapt to the learner’s level. So why is it that so many students are still being forced to modify themselves for the curriculum?
My children all have attended schools in the same public district. That district’s required math curriculum makes use of an idea called “Singapore math,” which is popular among the homeschool crowd and better known as “that blasted window thing” in my part of the world. In theory, the approach isn’t bad:
- Singapore students typically score well on international standardized math exams.
- The simplified matrix emphasizes the need to read the question prompt carefully, which reinforces literacy across the curriculum and promotes solid skills for taking standardized tests.
- The matrix asks students to conceptualize a story problem multiple ways, which feeds beautifully into differentiation.
Here’s the problem.
Students are not being taught in multiple manners. All kids must approach pretty much all math problems according to a drawn-out, four-step formula with no actual regard for students’ mastery levels or preferred learning styles. There is little to no choice.
Consider this first grade math problem:
Paul has 6 apples. Janice has 4 oranges. How many pieces of fruit do the children have all together?
After marking up the statement extensively by circling and underlining, here’s what the child must then do:
No, the kid can’t just say, “Hmm. Apples and oranges are fruit. 6 plus 4 is 10.” I have spoken with approximately 30 different parents who have students all across my district, and the four-step process is used consistently (and rigidly) in multiple buildings. Parents attend trainings so they can help their young elementary school students with math homework.
I don’t have a problem with different approaches to teaching math. I have a HUGE problem with this completely undifferentiated approach unless it quickly gives way to “you decide which parts of the window you need to solve the problem–you have to use at least 2.”
It takes much longer to work a single problem, so kids practice basic calculations far less than they do their printing and drawing skills. I know too many kids who sailed through elementary math with their windows and knew how to work specific word problems, but they did not understand the number concepts behind what they were doing. They simply memorized the approach so they would get good grades for showing their work, and once they hit algebra, they floundered (this would include my own kids). Worse, the four-step process has made some of my children HATE MATH. That’s probably what I can’t forgive, especially since it’s done under the guise of “differentiated instruction” and “higher order thinking” and other buzzwords.
This is not differentiated instruction. It is slowing math lessons down to the most basic level. It is forcing all kids to use manipulatives and visuals, when not all students are kinesthetic or visual learners. I agree wholeheartedly with Alexander Borisovich’s thoughts on many of the Singapore-math based books available in the U.S.:
The authors of the reviewed books will argue that they have the experience: many children won’t be able to understand this discussion, that they need the solution to be chopped into many steps, need to read and re-read the formulation of the problem, do it one sentence at a time, etc. Do not trust them — they are incompetent. They will tell you that word problems are hard because they contain words, and 2nd graders have difficult time understanding the words. Don’t buy it: The problem is stated concisely and clearly. The same children, when it comes to baseball, will talk in incomplete sentences 5 times faster that you can and understand each other perfectly. Word problems are hard not because they contain words, but because they require understanding of mathematics. To help the children who have difficulty with a problem, the teacher needs to understand what mathematics is needed in each problem.
There is no magic bullet for mathematical literacy, aside from a teacher with a strong foundation in the discipline and boundless confidence to meet each students where he or she is.