As promised, here is the second in a series of posts about the book Accessible Mathematics: 10 Instructional Shifts That Raise Student Achievement by Steven Leinwand.
The first instructional shift that Leinwand recommends is to incorporate ongoing cumulative review into every day’s lesson. The second shift is one that builds upon something that elementary teachers are already doing…
Instructional Shift 2: Adapt what we know works in our reading programs and apply it to mathematics instruction.
In reading, there is a careful progression from literal to inferential to evaluative comprehension. This is applied to all students. In reading instruction, many of the questions asked do not have a single correct answer, or do not have answers that come directly from the text but instead involve higher-order thinking skills.
Think for a minute about how different our typical approach to math instruction is from our approach to reading instruction. For example, going over homework at the beginning of class. It typically begins with, “Please get out your homework. Good. Joey? Nice work. Allison? Missing your homework again? Okay, here we go. Number 1. 33. Number 2. 47. Any questions? No? Great. Number 3…”
As Leinwand says, going over homework is typically “10 wasted, mindless minutes” of reading off correct answers that students really don’t care about. It is not accompanied by the ever important “Why?” and “How did you arrive at that answer?” type questions that are what really drive the learning in a math classroom.
All of math instruction, not just going over homework, really deserves another look. Good math instruction, like reading, begins with an answer. We don’t stop when we get the answer, we move beyond them into the extended comprehension.
How do we do this? First, limit the number of practice problems given for homework, or simply limit the number you actually go over in class. Choose a few that were difficult for students, or a few that really reinforce the learning from the previous lesson or set up the lesson for the day. Make sure the focus is on understanding and explanation, not on simply “checking the answers.” Second, all numerical and one-word answers should be consistently followed by a request for explanation or justification. Third, look at your own practice. Think about how you probe students in reading to really find out what they know. Parallel this practice in math as well. You’ll be amazed at what you see from your students.
If you want more detailed information about the parallels between reading and math instruction, another great book to check out is From Reading to Math: How Best Practices in Literacy Can Make You a Better Math Teacher by Maggie Siena. I have a copy in my office if anyone is interested in taking a look.