Mental Math Questions and Answers

Mental Math Questions and Answers

Draft -- January 2008

MENTAL MATH

Acknowledgements

The Department of Education gratefully acknowledges the contributions of the following individuals to the preparation of the Mental Math booklets:

Arlene Andrecyk--Cape Breton-Victoria Regional School Board Lois Boudreau--Annapolis Valley Regional School Board Sharon Boudreau--Cape Breton-Victoria Regional School Board Anne Boyd--Strait Regional School Board Joanne Cameron-- Nova Scotia Department of Education Estella Clayton--Halifax Regional School Board (Retired) Jane Chisholm--Tri-County Regional School Board Nancy Chisholm-- Nova Scotia Department of Education Fred Cole--Chignecto-Central Regional School Board Sally Connors--Halifax Regional School Board Paul Dennis--Chignecto-Central Regional School Board Christine Deveau--Chignecto-Central Regional School Board Th?r?se Forsythe --Annapolis Valley Regional School Board Dan Gilfoy--Halifax Regional School Board Robin Harris--Halifax Regional School Board Patsy Height-Lewis--Tri-County Regional School Board Keith Jordan--Strait Regional School Board Donna Karsten--Nova Scotia Department of Education Jill MacDonald--Annapolis Valley Regional School Board Sandra MacDonald--Halifax Regional School Board Ken MacInnis--Halifax Regional School Board (Retired) Ron MacLean--Cape Breton-Victoria Regional School Board (Retired) Marion MacLellan--Strait Regional School Board Tim McClare--Halifax Regional School Board Sharon McCready--Nova Scotia Department of Education David McKillop--Making Math Matter Inc. Janice Murray--Halifax Regional School Board Mary Osborne--Halifax Regional School Board (Retired) Martha Stewart--Annapolis Valley Regional School Board Sherene Sharpe--South Shore Regional School Board Brad Pemberton--Annapolis Valley Regional School Board Angela West--Halifax Regional School Board Susan Wilkie--Halifax Regional School Board

QUESTIONS AND ANSWERS -- DRAFT JANUARY 2008

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Contents

General Questions about Mental Computation G1. What is mental math?................................................................................................ 1 G2. What is mental computation?.................................................................................... 1 G3. How are the terms fact learning, mental calculations, and computational estimation related?..................................................................................................... 2 G4. Why is so much attention being given to fact learning, mental calculation, and estimation? ......................................................................................................... 2 G5. What is fact learning in mental computation?............................................................ 2 G6. What is mental calculation? ....................................................................................... 2 G7. What is computational estimation?............................................................................ 2 G8. What are two principles that guide the development of mental computation? .......... 3 G9. What are compatible numbers, friendly numbers, and nice numbers? ....................... 3 G10. What is measurement estimation? ............................................................................. 3 G11. What is spatial sense?................................................................................................. 3 G12. Should you devote the same amount of time every day to mental math? ................... 3 G13. How many strategies are there at each grade level? .................................................... 4 G14. How supportive of mental math are the currently available resources? ...................... 4 G15. What should I do if my students cannot do the strategies assigned to my grade? ............................................................................................... 4

Questions about Teaching Mental Computation T1. Is there a general approach to mental computation that should be taken? ................. 5 T2. Is there something you should do first when you want to introduce a new strategy? . 6 T3. How complex should the numbers be in mental computation exercises? ................... 6 T4. How important is the selection of the exercises to apply the strategies? ..................... 6 T5. What should practice exercises look like? .................................................................. 6 T6. Should the practice exercises be presented orally or visually? ..................................... 7 T7. How quickly should you expect students to get answers? .......................................... 7 T8. Should you expect students to record only their answers in mental computation exercises? ............................................................................................. 8 T9. Do you force students to use a strategy when they already have an alternative strategy to get the answer? ........................................................................................ 8 T10. Will you see students using the strategies just the way we teach them? ...................... 8 T11. Do the students need to know the names of the strategies? ....................................... 8 T12. Does the mental math you do daily have to be connected to your main lesson? ........ 9 T13. How can you help students to use and apply mental computation strategies beyond the allocated mental math time? ................................................................... 9 T14. What role can parents/guardians play in the development of mental computations? . 9 T15. Is there a general approach to measurement estimation? .......................................... 10 T16. Is there a general approach to teaching spatial sense? ............................................... 11

Questions about Adaptations and Assessment A1. How do I differentiate instruction in mental computation? .................................... 12 A2. What does mental computation look like in a multi-age or combined grade classroom? ..................................................................................................... 12 A3. What does assessment of mental computation look like? ......................................... 12 A4. Are timed tests, such as the Mad Minutes program, supportive of our goals in fact learning? .......................................................................................................... 14

MENTAL MATH

General Questions about Mental Computation

G1. What is mental math?

In the mathematics education literature, there is not consensus on the usage of some of the words and expressions in mental math. In order to provide uniformity in communication in these booklets, it is important that some of these terms be defined. For example, the Department of Education in Nova Scotia uses the term mental math to encompass the whole range of mental processing in all strands of the mathematics curriculum. Mental math is broken into three categories in the grade-level booklets: mental computation, measurement estimation, and spatial sense. Mental computation is further broken down into fact learning, mental calculation, and computational estimation.

MENTAL MATH

Mental Computation

Measurement Estimation

Fact Learning

Spatial Sense

Mental Calculations

Computational Estimation

Although it is important to incorporate some aspect of Mental Math into your mathematics planning every day, the time spent each day may vary. While the Time to Learn document requires 5 minutes per day, there will be days, especially when introducing strategies, when more time will be needed. Other times, such as when reinforcing a strategy, it may not take 5 minutes to do the practice exercises and discuss the strategies and answers.

G2. What is mental computation?

Mental computation deals with fact learning, mental calculations and computational estimation across the strands. This covers mental math found primarily in the General Curriculum Outcomes (GCO) B. Contexts for using mental computation can be found in the six other GCO's and includes measurement estimations, quantity estimations, patterns and spatial sense. For more information on these and other strategies, see Elementary and Middle School Mathematics: Teaching Developmentally by John Van de Walle.

QUESTIONS AND ANSWERS -- DRAFT JANUARY 2008

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MENTAL MATH

G3. How are the terms fact learning, mental calculations, and computational estimation related?

While each category in computations has been defined separately, this does not suggest that the three categories are entirely separable. Initially, students develop and use strategies to get quick recall of the facts. These strategies and the facts themselves are the foundations for the development of other mental calculation strategies. When the facts are automatic, students are no longer employing strategies to retrieve them from memory. In turn, the facts and mental calculation strategies are the foundations for computational estimation strategies. Actually, attempts at computational estimation are often thwarted by the lack of knowledge of the related facts and mental calculation strategies.

G4. Why is so much attention being given to fact learning, mental calculation, and estimation?

In modern society, the development of fact, mental calculations, and computational estimation strategies needs to be the major goals of any computational program for two major reasons. First of all, in their day-to-day activities, most people's calculation needs can be met by having well developed mental computational processes. Secondly, while technology has replaced paper-and-pencil as the major tool for complex computations, people need to have well developed mental strategies to be alert to the reasonableness of answers generated by technology. Besides being the foundation of the development of number and operation sense, fact learning itself is critical to the overall development of mathematics. Mathematics is about patterns and relationships and many of these patterns and relationships are numerical. Without a command of the basic relationships among numbers (facts), it is very difficult to detect these patterns and relationships. Nothing empowers students with confidence and flexibility of thinking more than a command of the number facts.

G5. What is fact learning in mental computation?

Fact learning refers to the acquisition of the 100 number facts related to the single digits 0 to 9 for each of the four operations. When students know these facts, they can quickly retrieve them from memory (usually in 3 seconds or less). Ideally, through practice over time, students will achieve automaticity; that is, they will have instant recall without using strategies.

G6. What is mental calculation?

Mental calculation refers to using strategies to get exact answers by doing all the calculations in one's head. This is the definition we are using in Nova Scotia; you may find the term used elsewhere to include fact learning and estimation.

G7. What is computational estimation?

Computational estimation refers to using strategies to get approximate answers by doing calculations in one's head.

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QUESTIONS AND ANSWERS -- DRAFT JANUARY 2008

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