Accessible Mathematics – Part 1

I’ve just started reading the book Accessible Mathematics by Steve Leinwand.  Steve is Principal Research Analyst at the American Institutes for Research in Washington, D.C., where he supports a range of mathematics education initiatives and research. Steve served as Mathematics Supervisor in the Connecticut Department of Education for twenty-two years and is a former president of NCSM.

In this book, Steve takes a look at 10 instructional shifts that can have great effects on student achievement.   As I read through the book, I’ll share those 10 shifts with you here on the blog.

I attended one of Steve’s workshops several years ago, and used some of his ideas in my classroom – and have now passed them on in my role as a math coach. This first instructional shift is the idea I used most often in my own classroom.

Instructional Shift 1: Incorporate ongoing cumulative review into every day’s lesson.

Almost nobody masters a new skill in just one lesson or one assignment.  The key to this strategy is to keep bringing skills back day after day, week after week throughout the year to ensure mastery.  This can be done in many different ways – problem of the day, warm-ups, oral/slate activities, or what Steve calls “mini-math”, which is what I used in my classroom after learning about it in the workshop.

“Mini-math” is a six question oral quiz, where each question is read twice. This can be done while checking to see that everyone has done homework, or even while checking attendance.  The example Steve gives in the book is the following – for a sixth-grade class:


1. 6 x 7

2. What number is 1000 less than 18,294?

3. About how much is $0.29 and $0.32?

4. What is 1/10 of 450?

5. Draw a picture of 1 2/3

6. Estimate my weight in kilograms.

Each question is read to the class twice while they answer on small sheets of paper.  Of course, this can be adapted to meet the needs of diverse learners.  Some may need the questions printed in front of them, while others are fine with the auditory nature of this particular activity.  There may be times where you put a word problem up on the board as one of the questions, or you may need to print out sheets with a geometric figure to have students answer a question.

If you notice, there is quite a variety in the types of questions asked.  There is a reason for this.  The first is a basic fact. This particular fact was chosen because students were still having trouble with the x7 tables.  This question can change during the year depending on the facts your class is working on – addition, subtraction, multiplication or division.

The second question is a place value question. This was chosen based on the fact that the place value chapter was a while ago, and the teacher wanted to make sure students remember what was covered.  This can also be used to extend the understanding of place value by using 100 more/less, 1000 more/less and 10,000 more/less than the given number.

The third question is an estimation question – and as we all know, estimation is often a sticking point for our students.  This could be a simple, whole number estimation problem or a more difficult one using money – like the example given.  Having students estimate daily is a great way to improve performance in this area.

The fourth question is building upon basic facts, moving on to the skills of multiplying and dividing numbers by 10, 100, and 1000.

The fifth question is important because it is a way to have students develop their conceptual understanding of mathematics by using a concrete representation.  Having students draw a model for a number – whether it be a whole number or a fraction – reinforces this idea.

The sixth question is a measurement question – which Steve says “is often the lost strand of the mathematics curriculum.” Depending on what you’ve covered in class, this could be a question on length, weight, capacity, area, perimeter, metric, or standard measurement.

Now, do you buy the strategy? Six quick questions that can review all of those different areas? I bought it hook, line and sinker during my last year in the classroom. It was an amazing tool for me as a teacher to ensure students were continually exposed to the important ideas they needed to secure, and it also alerted me to when kids just weren’t getting it.  Give it a try.  See how “mini-math” can help you in your classroom.  Want some help developing some “mini-math” questions for your class? I’d be glad to help.

About gpsmathcoach

I am an Elementary Math Coach for the Greenwich Public Schools in Greenwich, Connecticut. I serve 11 elementary schools and approximately 240 teachers.
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