Tuesday / June 25

# Teaching for Understanding: 6 Strategies for Helping All Students Learn Basic Math Facts

One of the topics in mathematics education that has caused a flurry of debate is whether students should know their basic mathematics facts from memory—meaning they can automatically give the answer to any fact. This question is not new—you can find it in educational publications, on the web, and debated among K-12 classroom teachers. In my 43 years of teaching mathematics in K-8 and working with K-12 teachers, the question continues to come up. The expectations have not changed with new standards. Perhaps the wording “fluency” vs. “mastery” has prompted some concern. However, the fact is that students must know their basic facts from memory, which means that the ultimate goal is quick recall.

Brain research shows that when students know their basic facts, they free up working memory in order to attend to a more difficult task at hand. We also know that students who enter the middle grades knowing their basic facts are more likely to be successful with more complex math concepts. The Common Core and other College and Career Ready Standards clearly state that students must be fluent with basic math facts and go so far as to indicate at what grade levels this should happen.

I think we are asking the wrong question. It is not whether students should be proficient with basic facts. Rather, the question should be: How do we, as teachers, better ensure student success with learning basic facts through better instructional practices?

Here are some research based suggestions that have added benefits beyond just fact memorization:

### 6 Strategies for Teaching Basic Math Facts

1. Teach basic facts within the context of understanding the operations and mathematical properties. Tables 1 and 2 in the Common Core State Standards for Mathematics (pages 88 and 89) provide a powerful model for this approach.
1. Help students to develop strategies (using mathematically sound approaches instead of “tricks”) for thinking flexibly about facts that are “easy” (3 + 1, 8 – 2, 1 x 7, 9 ÷ 1) and facts that are challenging (8 + 6, 17 – 9, 6 x 7, 56 ÷ 7). Build on operational understanding and mathematical properties. For example, if students know the combinations that make ten, they can use that knowledge to figure out 8 + 6 by thinking 8 + 2 + 4.
1. Give students time to practice facts using strategy retrieval. Use non-competitive games and activities that do not emphasize speed. If you play the age-old game “Around the World” with flash cards, think about who is really getting the practice… yep, the kids who already know their facts! Some students need more processing time as they begin to work toward quick recall. Emphasizing speed early on doesn’t do much more than build anxiety.
1. Stop using timed tests! Consider alternate methods for assessing student proficiency. You know your expectations—observe a group of students play a game that focuses on a particular set of facts and make note of those students who need more practice. It is okay for students to use worksheets to practice facts, but be reasonable. How often in real life does anyone need to regurgitate 50 or 100 facts at one time? Give students 15 facts. Don’t time them (but you can watch them!). First, focus on accuracy. Have students keep record of the facts they need to practice.
1. Use purposeful questions to support student strategic thinking. (What do you know that can help you to find the sum of 9 + 7? What does 4 x 8 mean? How many groups of 6 can you make from 48? Can you make 5? 7?)
1. Upper grade teachers, you may likely have to spend some time reviewing facts. Use quick probes to see which facts kids have mastered and which they may still need to practice. If a strong foundation has been laid in the earlier grades, you should not have to take time re-teaching the facts. The reality is that in everyday life students don’t use basic facts very often. (You can give parents suggestions for helping them remember over long breaks!) Plan to spend some time reviewing and make explicit connections to other concepts, such as finding area, perimeter or volume of a figure, studying factors, multiples, primes and composite numbers, and multiplying and dividing by multiples of ten.

The question is not “Do kids need to know their basic facts?” Of course they do! That is not negotiable. The question is, “How can we support student thinking and understanding so that the initial work focuses on mathematical understanding, patterns, and thinking? How do we connect that to meaningful (anxiety-free) practice?”

This all takes time and some rethinking about our own instructional practice. It is worth the effort! The result will be students who are proficient with basic facts and maybe have even developed some positive attitudes about doing mathematics along the way!

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Winner of the Presidential Award for Excellence in Science and Mathematics Teaching, Linda M. Gojak directed the Center for Mathematics and Science Education, Teaching, and Technology (CMSETT) at John Carroll University for 16 years. She has spent 28 years teaching elementary and middle school mathematics, and has served as the president of the National Council of Teachers of Mathematics (NCTM), the National Council of Supervisors of Mathematics (NCSM), and the Ohio Council of Teachers of Mathematics. She is all about getting K-8 teachers and students active and excited about learning and doing mathematics. Her presentations are extremely practical. Teachers and administrators leave with many ideas for implementing effective teaching practices in the mathematics classroom. At the same time, she values and integrates the importance of building deep understanding of mathematics and ways to meet the needs of students at all levels of achievement. Building conceptual understanding of mathematical ideas and problem solving sit at the core of expertise. Linda is co-author of The Common Core Mathematics Companion: The Standards Decoded, Grades K-2 and The Common Core Mathematics Companion: The Standards Decoded, Grades 3-5. Follow her on Twitter: @LindaGojak