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| Didax "Class Ideas" Newsletter Archive |
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Since this is our first newsletter since June, we hope all of you had a great summer and are happy to be back in school. Our October issue brings lots of treats and no tricks!
This month, we're pleased to introduce an all-new edition of Didax?s popular Daily Mental Math series for Grades 2?7. This fun, fast math refresher course is an ideal way to reintroduce key math concepts as the new school year gets underway, so be sure to take a look at the downloadable activity pages from each of the six books in the series. And if you're an email subscriber, don't miss our super October special on these books!
As always, I'd love to hear your ideas for topics you'd like to see in future newsletters, so please don't hesitate to email me.
Cindy O'Neill, Editor |
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| Daily Mental Math: Flexible Strategies That Work |
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 Good teachers know the importance of regular mental mathematics sessions. In fact, the pendulum has swung back in favor of mental math in today?s classrooms, but it is not the old drill-and-skill methods that are encouraged. Instead, the focus is on the development of flexible mental strategies.
What is a mental strategy?
Simply put, mental strategies are the methods we use to turn a ?calculation we cannot do into a calculation we can do by employing relationships between numbers and operations? (McIntosh, Reys, & Reys, 1997). For example, a common strategy for solving questions mentally is to derive an answer from an already known fact. Students who cannot recall that 7 x 6 = 42 may remember that 6 x 6 = 36. From there, it's a simple step to work out that 7 x 6 is 36 plus another 6.
Many different mental strategies have been identified, such as the ?near doubles? strategy or the ?make to ten strategy.? For instance, when adding 8 and 7, students might use their knowledge that double 8 is 16 and 8 + 7 would be one less, or that double 7 is 14 and 8 + 7 would be one more, or 15. It is not important to know the names of all the various strategies that students might use when performing a mental calculation, but rather that students will differ in their approaches to mental calculation.
The following are some suggestions for making flexible strategies the basis of a successful mental mathematics program in your classroom.
Have students share their mental strategies.
Current research suggests that students should be encouraged to share the mental strategies they use to solve questions independently and with the assistance of their peers. You can promote this sharing by providing a classroom atmosphere where the open discussion of mental strategies is encouraged. Research from the United Kingdom found that good teachers of numeracy played an active role in this discussion. Rather than telling students what methods to use or supplying them with rules, these teachers helped their students to make connections:
?The only way to find out how students calculate mentally is to ask them to explain their thoughts much the same way as you would in a brainstorming session. As with brainstorming, it is important that students feel their contribution is valued. Over time students become so familiar with certain calculations that they become known facts that may be retrieved from memory? (Askew, 1998).
Refrain from introducing rules.
Students should be given the opportunity to develop their own flexible mental strategies and then to share them. There is a danger that, in our attempts as teachers to help students develop strategies, we might shortcut the process by introducing rules or tricks. For example, when multiplying 3 x 80, it may be tempting to introduce a rule involving ?taking off zeros? and ?adding zeros? to help students develop an efficient strategy for dealing with this type of calculation. Unfortunately, unless a student is ready for such a strategy, he/she may start using it because the ?teacher has shown me,? without any understanding of why it works. It is better to resist the temptation to shortcut the process of students developing strategies and, instead, set up opportunities that allow them to discover, on their own, patterns that help them make calculations.
Strive for fluency of recall.
Any daily mental math program should strive for fluency of recall rather than instantaneous or instant recall, as these latter terms conjure up images of rapid-fire questions being called out to students and rapid-fire answers being given in response. If you pause for a moment to consider the result of this practice, you'll realize that little or no time is allowed for students to work out the answers in their head. Either students know the answer or they don?t. Also consider your own thought processes. How well do you handle pressure? When put under pressure, students may know the answer, but fear takes over and they ?forget? it.
It is better to aim for fluency of response, which is similar to being fluent in the use of a language. At times we may stutter or stumble or perhaps have a word on the tip of our tongue, but as long as we can make ourselves understood, we have achieved our goal. The aim of mental computation should be to support the more difficult mental calculations, and then the informal written methods, and eventually the more formal written methods students will be expected to use. In each case, students will need to be fluent in their use of basic number facts but not necessarily offer an instant response.
Focus on the mathematics needed in real life.
If our mental math sessions focus solely on the 390 basic number facts, we will be selling our students short. Surveys of computations carried out by adults in their daily life indicate that much more is required than simply recalling basic number facts. One survey in Australia found that more than 80% of these calculations involved mental math and that many of these calculations occurred in context. Other research showed was that almost 25% of the mental calculations adults made were related to time (Northcote and McIntosh, 1999). One further finding of interest to teachers is that the majority of calculations performed by adults involved addition (46%) and subtraction (42%). Yet, mental mathematics programs often focus on the development of basic multiplication facts or tables.
In summary, by giving your students the opportunity to share their mental math strategies with their peers and not introducing rules before students are ready for them, and keeping the focus on fluency of recall within the context of real-life math problems, you will be well on your way to providing your students with the foundation they need to become math-literate adults.
References:
Askew, M. (1998). Teaching Primary Mathematics: A guide for newly qualified & student teachers. Great Britain: Hodder & Stoughton, 50.
McIntosh, A., Reys, R., Reys, B.(1997). Mental computation in the middle grades: The importance of thinking strategies. Mathematics in the Middle School, 2 (5), 323.
Northcote, M., McIntosh, A. (1999). What mathematics do adults REALLY do in everyday life? Australian Primary Mathematics Classroom, 4 (1), 19?21. |
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| Downloadable Daily Mental Math Activity Pages |
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 This month we're offering sample activity pages from each of the six books in the Daily Mental Math, 2nd Edition series. That's a whole week's worth of mental math activities for each book!
This 40-week program of daily exercises and weekly assessments uses real-world contexts (telling time, making change, and more) to help students learn all 390 basic number facts. Questions are posed in varied language to boost mathematics vocabulary. Download these pages to try the Daily Mental Math approach in your classroom! |
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| Mental Math Internet Links |
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 If you're looking for some fun mental math exercises to do on the computer, these links will help you get started. Keyed-In Magazine offers links to games and test versions of mental math exercises in addition, subtraction, multiplication, division, and percentages. Or try your luck at the "Function Machine Game." For the thinking behind the mental math approach, read the NCTM article on why these mental gymnastics play such a valuable part in students' mathematics learning. Enjoy! |
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| November Newsletter Theme: Early Childhood Math |
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 Next month we'll explore the fascinating theme of early childhood math through the eyes of noted author and educator Kathy Richardson. In her just published book Developing Math Concepts in Pre-Kindergarten, Kathy shows teachers how to actively engage young students so they can meaningfully develop these foundational ideas. We promise an issue packed with information and activities you can use in your pre-K classroom as well as a great special on this wonderful new classroom resource. Until then, happy Halloween! |
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