Helping with Math at Home

Transcription

1 Helping with Math at Home Ideas for Parents Workshop Handout Masters (Click on title to access PDF) Handout 1 What Can Parents Do... Handout 2 Practicing Numerical Reasoning Handout 3 Multiples of 5 Dominoes Game Handout 4 Blackline Master of Double-6 Domino Set Handout 5 The Game of Skunk Handout 6 Thinking About Skunk Handout 7 Pig/Get to Zero Handout 8 Math Games for Family Fun Handout 9 X/O Problem Handout 10 Parents as Questioners Handout 11 Helping Your Child with Mathematics Handout 12 But I Don't Have Time to Wait for You to Learn! Handout 13 Research Brief Handout 14 Feedback Form

2 Workshop Handout Masters (English)

3 What Can Parents Do with Your Child... for Your Child... as an Adult?... as a Parent? at Home? at School? Parent as a Learner continue to learn and be a learner of mathematics recognize that mathematics is an important tool for making sense of the world around you recognize that new discoveries are still being made in mathematics learn what math is all about for your child pay attention to experiences that impact your child s attitudes about mathematics investigate and play with numbers involve your child in the measuring and comparing that you do at home use games to support mathematical thinking do mental arithmetic and share strategies attend parent math nights look for information that comes home about your school s mathematics program become familiar with mathematics as it is taught in your child s classroom Parent as a Researcher be curious about how you and others solve problems broaden your understanding of what mathematics is find out about current research in mathematics teaching and learning ask questions to understand your child s thinking be curious about how your child solves problems investigate with your child his or her mathematical questions explore with your child the best time and place to do homework ask questions about your child s mathematics program, both the goals and how it is taught find out about roles for parents in the mathematics program at your child s school Parent as a Communicator recognize that learning and understanding mathematics depends on communication (listening, talking, and writing) learn to examine and explain your own thinking share information with your child about how you use mathematics display a positive disposition about mathematics talk with your child about the importance of mathematics in his or her life explore the many ways to approach solving problems be clear about your expectations for homework find a way to let the school know what you want for your child s mathematical education become a knowledgeable advocate for good mathematics education find ways to show enthusiasm about mathematics Handout 1 Helping with Math at Home: Ideas for Parents HANDOUT 1

4 Handout 2 Practicing Numerical Reasoning Directions: Solve these problems mentally without using paper and pencil = = 7 8 is 56. If someone did not know this multiplication fact, how could he think about it? Write as many ideas as you can. HANDOUT 2 Helping with Math at Home: Ideas for Parents

5 Handout 3 Multiples of 5 Dominoes Game You Will Need A double-six set of dominoes (the game is more challenging if you play with a double-nine set of dominoes). Object of the Game Play each tile so that the end sums numbers at the ends of the domino train add up to 5 or a multiple of 5. Maintain cumulative scores for each player. The highest score wins. How to Play Set all dominoes face down in a kitty. Each player takes seven dominoes from the kitty. The player with the highest double plays first. After each play, players add the end sums sum of the numbers at each ends of the domino train. If the player scores (the sum of the numbers is 5 or a multiple of 5), the player records the sum and continues to play another domino and gets to play again until the end sum is not a multiple of 5. Cumulative scoring is recorded after each tile is played. The next player then puts his tiles in play. Players who do not have a domino that can be played when it is their turn must draw single dominoes from the kitty until they pick a domino that can be played. The game is over if a player plays all of the dominoes in his or her hand. The player who plays the last domino also receives the sum of all of the other dominoes remaining in the other players hands. The player with the most points at the end is the winner. Note: An electronic version of the game of dominoes is available on AOL (games). Helping with Math at Home: Ideas for Parents HANDOUT 3

6 Handout 4 Blackline Master of Double-6 Domino Set HANDOUT 4 Helping with Math at Home: Ideas for Parents

7 Handout 5 The Game of Skunk You Will Need two or more players (more than five is best) two dice Object of the Game Determine at what point in rolling the dice it is best to save your cumulative score. The highest score wins. How to Play Each player writes Skunk in big letters on a paper. The game involves five rounds, one round for each letter in Skunk. First, everyone stands up for the letter S. The dice are rolled (for example, shows a 6). Each standing player has a choice either sit down and take those points and record them under the letter S or continue standing for another roll of the die. Players can stand as long as they want for additional rolls of the die, adding the new roll for their current sum for that letter. A player must choose to sit down and keep his or her sum before a roll, not after. The die is rolled for a particular letter until no one is left standing. But beware! Anyone still standing when a 1 is rolled (on either die) loses all points and receives a score of 0 for that letter. A new round (for example, for the next letter K) begins after either roll of a 1 or everyone has chosen to sit down to preserve their score. After the five rounds, players add their scores, and the highest total wins. Helping with Math at Home: Ideas for Parents HANDOUT 5

8 Handout 6 Thinking About Skunk Choice vs. Chance 1. Skunk is a game that involves both choice and chance. What part of Skunk involves choice? What part of the game involves chance? 2. List some other games you know. Which games involve mostly choice? Which games involve mostly chance? Rate each game on a scale of 1 to 10 with 1 = pure chance 5 = chance/choice about equal 10 = pure choice 3. In life many things happen. Some are the result mostly of chance or luck, and others mostly result from choices or decisions you make. Think about some things that happened recently in your life. List two things that happened to you mainly due to chance. List two things that happened mostly because you made a choice. Investigate the Following in Depth 1. Rolling a 1 in Skunk is a disaster. To get a better score it is useful to know, on average, how many good rolls happen in a row before a 1 or double-1 comes up. Decide on a way to find this out. Carry out your plan and describe the results. 2. In Skunk, when a 1 does not come up, what is the average score on a single roll of a pair of dice? Decide on a way to find this out. Carry out your plan and describe the results. 3. What are some strategies that could be used to play Skunk? Describe a play-it-safe strategy. Describe a risky strategy. Estimate the kinds of scores each strategy would be likely to produce. Play Skunk using each of your strategies and keep a record of your scores. How well do your results agree with what you expected. Why should these strategies be tested in many games? Adapted from Choice and Chance in Life, by D. Brutlag. EDC, Used with permission. HANDOUT by Mathematics Education Collaborative From Helping from Helping with Math with Math Home: at Home: Ideas Ideas for Parents. for Parents Portsmouth, NH: Heinemann. Helping with Math at Home: Ideas for Parents

9 Handout 7 Pig You Will Need two or more players two dice How to Play The goal is to be the first player to reach 100. On your turn, roll the dice and determine the sum. You can either stop and record that sum or continue rolling and add the new sums together. Roll the pair of dice as many times as you choose. Again, when you decide to stop, record the current total for your score (and add it to your previous score). But beware! If you roll a 1 on exactly one die, your turn ends and 0 is your recorded score for that turn. And, if you roll double 1s, your turn ends and your entire score is set back to 0. Adapted from About Teaching Mathematics by Marilyn Burns. Copyright 2000 by Math Solutions Publications. Reprinted with permission. All rights reserved. You Will Need two or three players three dice Get to Zero How to Play First, on a sheet of paper, each player needs to write the players names and the number 999 under them. A player rolls the three dice, then arranges the three numbers (for example, 2, 3, 5) in some order (for example, 235, 352, 532, and so on) and subtracts that 3-digit number from 999. The other players also should subtract as a check. The players take turns, rolling the die to make their special number and continuing to subtract. The winner is the first player to reach 0, but they must get to 0 exactly. At any time, a player may choose to roll only one or two dice, instead of three dice. If the only numbers a player can make are larger that his remaining score, the player loses his turn. See About Teaching Mathematics (Math Solutions Publications, 2000) for additional games that support arithmetical skills. Adapted from Burns, Marilyn, The Math Solution. Not in print. From 2006 Helping by Mathematics with at Education Home: Ideas Collaborative for Parents. from Helping Portsmouth, with Math NH: Heinemann. at Home: Ideas for Parents. Portsmouth, NH: Heinemann. Helping with Math at Home: Ideas for Parents HANDOUT 7

10 Handout 8 Math Games for Family Fun Compiled by Ruth Parker Mathematics Education Collaborative mec@mec-math.org Website: mec-math.org Parents have asked me to recommend some good games that encourage math play at home. It s a question I love to be asked. How math is experienced in the home has a big impact on how children do with math at school. As the math auntie of quite a few nieces and nephews, I m always looking for challenging and fun math games games that engage children in mathematical reasoning and help them experience the compelling nature of a good math challenge. I ve polled my nieces and nephews and can offer some of our favorites (most are available in toy stores and in price range $5 to $15). Set: A card game of logic and visual perception that can be enjoyed by the whole family (ages 6 to adult). Adults... be forewarned that it can be humbling to play this game with youngsters. Tangos: A game that focuses on spatial relationships that will provide challenges to the whole family, young and old alike. Mastermind: A game of logic that can be enjoyed by both children and adults. Look for a version of Mastermind for younger children (ages 6 and up). Cribbage: A card game that s played on a pegged board and is wonderful for developing skill in adding series of small numbers. The game is enjoyable for children of all ages. Dominoes: A game of strategy and numbers that can be played with children as young as 4 years of age as a number recognition game, and yet the regular game of dominoes is challenging for adults as well. Mancala: An African stone game of logic that is challenging for adults but can be adapted to meet the needs of children ages 5 and up. Equate: A game for reinforcing computation with whole numbers, decimals, and fractions. I haven t played this yet, but my nieces and nephews tell me it is challenging and fun. Checkers/Chess: Great games for developing skill with logical reasoning. We hope you find these math games as fun as we do. Curl up with your favorite kid(s) and enjoy playing math. Please let us know if you have other favorites to add to the list. HANDOUT 8 Helping with Math at Home: Ideas for Parents

11 Handout 9 X/O Problem You have three cards marked as follows: one card with an X on both sides one card with an O on both sides one card with an X on one side and an O on the other Suppose all three of these cards are in a bag. You reach into the bag, randomly draw a card, and you are looking at an X. Is it more likely that the other side will show an O? An X? Or, are both equally likely? Helping with Math at Home: Ideas for Parents HANDOUT 9

12 Handout 10 Parents as Questioners Mathematical investigations present new and sometimes unexpected mathematical situations, so the teacher cannot have taught the way to solve the problem in advance. The student needs to apply prior knowledge in ways that make sense to the situation. There may be many paths to follow and many outcomes, depending on the problem; the student must make his or her own plan for finding a solution. Parents can assist their children to be independent problem solvers by becoming guides or questioners. They do not need to know how to solve the problem themselves, but can help the students think through the problem and make a realistic plan for solving it. USE FREELY any questions that will help students think about the way they are tackling the problem: What have you tried? Is there another way to look at the problem? Can you explain this to me? What makes sense so far? Is there another way to think about it? Is this like any other problem that you have worked on in any way? What is it you are trying to do/solve/find out? USE SPARINGLY those questions that tend to direct students thinking: How might you organize this? Can you make a table of your results? Can you see any patterns? Have you tried smaller (or simpler) cases? How can you start? Have you checked to see that the solution works? What would happen if...? AVOID any hint or question referring to the particular problem: Do you recognize square numbers? Explore it like this... Why not try three counters? That s not quite what I had in mind... No, you should... Adapted from Shell Centre for Mathematical Education's Problems with Pattern and Numbers (1984, 2001, see HANDOUT by Mathematics Education Collaborative From Helping from Helping with Math with Math Home: at Home: Ideas Ideas for Parents. for Parents Portsmouth, NH: Heinemann. Helping with Math at Home: Ideas for Parents

13 Handout 11 Helping Your Child with Mathematics Be a Learner Yourself Learn to play with numbers using mental arithmetic. Play mathematical games at home that involve problem solving. Notice when you use mathematics in your everyday life and share this with your child. Demonstrate that you value persistence. Get to know the research on math education. Be a Researcher Become a question poser. Be curious about your child s thinking when he or she is doing math. Be a thoughtful listener. Ask questions that help you understand your child s thinking. Know that teaching by telling is not how people learn mathematics. Be a Communicator Recognize how important talking and writing are to learning mathematics. Talk with your child about the many ways to think about a math problem. Encourage diverse ways of solving problems. Helping with Math at Home: Ideas for Parents HANDOUT 11

14 Handout 12 But I Don t Have Time to Wait for You to Learn! Reflections on What It Really Means to Raise Expectations Kathy Richardson Math Perspectives Teacher Development Center Bellingham, WA During this time in education when the emphasis is on high expectations and accountability, it is essential that we stop and reflect on what this means in the lives of individual children. The need to be successful in mathematics is becoming increasingly important for all children. It is true that children can learn more than we thought possible in years past but only if they are allowed the time and experiences they need to understand the mathematics they are learning. When the pressure is on, there is a temptation to get the kids to do it. Too often we end up creating illusions of learning rather than building the solid foundation that helps the children continue to move forward after they leave us. We must find ways to meet children where they are in their learning and not demand they perform beyond what they can do with understanding and competence. No matter what external pressures we feel, we must stay focused on providing children with the experiences that will be most appropriate for them. The following are quotes I have gathered from various places that help me remember how important our job is and to whom we are most accountable. The mathematical experiences of a child before the age of eleven, and the responses he has been encouraged to make to them, largely determine his potential mathematical development.... The learning of mathematics in the widest sense, begins before the child goes to school and continues throughout the primary (elementary) school and beyond. (Notes on Mathematics in Primary Schools, p. 1) Virtually all young children like mathematics. They do mathematics naturally, discovering patterns and making conjectures based on observation. Natural curiosity is a powerful teacher, especially for mathematics. Unfortunately, as children become socialized by school and society, they begin to view mathematics as a rigid system of externally dictated rules governed by standards of accuracy, speed, and memory. Their view of mathematics shifts gradually from enthusiasm to apprehension, from confidence to fear. Eventually, most students leave mathematics under duress, convinced that only geniuses can learn it. (National Research Council, Everybody Counts, p. 44) More than any other subject, mathematics filters students out of programs leading to scientific and professional careers.... Mathematics is the worst curricular villain in driving students to failure in school. When mathematics acts as a filter, it not only filters students out of careers, but frequently out of school itself. (National Research Council, Everybody Counts, p. 7) No matter what the age or ability of the students, their experiences with mathematics teach them something about themselves and their place in the world. (K. Richardson, Calif. State Dept. of Ed., Math Model Curriculum Guide K 8, p. 11) Kathy Richardson, Math Perspectives, Bellingham, WA HANDOUT by Mathematics Education Collaborative From Helping from Helping with Math with Math Home: at Home: Ideas Ideas for Parents. for Parents Portsmouth, NH: Heinemann. Helping with Math at Home: Ideas for Parents

15 Handout 13 Research Brief National Research Council. (2001). Adding It Up: Helping Children Learn Mathematics. J. Kilpatrick, J. Swafford, and B. Findell (Eds.). Mathematics Learning Study Committee, Center for Education, Division of Behavioral and Social Sciences and Education, Washington DC: National Academy Press. Excerpts: This report was approved by the Governing Board of the National Research Council, whose members are drawn from the Councils of the National Academy of Sciences, the National Academy of Engineering, and the Institute of Medicine. The members of the committee responsible for the report were chosen for their special competences with regard for appropriate balance. They were given the following charges: to synthesize the rich and diverse research on prekindergarten through eighth-grade mathematics learning to provide research-based recommendations for teaching, teacher education, and curriculum for improving student learning and to identify areas where research is needed to give advice and guidance to educators, researchers, publishers, policy makers, and parents Adding It Up addresses many questions: What exactly do we know from research about the teaching and learning of mathematics? And what does this research really tell us? Should children learn computation methods before they understand the concepts? What is the role of concrete manipulatives? Do teachers and student expectations make a difference? The conclusions and recommendations drawn from this report of the research provide us with information about improving the teaching and learning of mathematics. Selected Quotes: Knowledge that has been learned with understanding provides the basis for generating new knowledge and for solving new and unfamiliar problems. When students have acquired conceptual understanding in an area of mathematics, they see the connections among concepts and procedures and can give arguments to explain why some facts are consequences of others. They gain confidence, which then provides a base from which they can move to another level of understanding. (p. 119) A significant indicator of conceptual understanding is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes. (p. 119) Helping with Math at Home: Ideas for Parents HANDOUT 13

16 Connections are most useful when they link related concepts and methods in appropriate ways. Mnemonic techniques learned by rote may provide connections among ideas that make it easier to perform mathematical operations, but they also may not lead to understanding. These are not the kinds of connections that best promote the acquisition of mathematical proficiency. (p. 119) Washington State Office of the Superintendent of Public Instruction. (2000). Teaching and Learning Mathematics: Using Research to Shift From the Yesterday Mind to the Tomorrow Mind. J. Johnson (Ed.). Excerpts: This book provides an overview of the potential and challenges of teaching quality mathematics (K 12). A good portion of it summarizes some of the research results, in a very concise format, related to each of the essential learning academic requirements in mathematics. It is a resource text designed to serve as a catalyst for promoting reflection, discussion, and problem solving within the education community, and to help educators become knowledgeable about available research results and ways they can be integrated into the classroom. It is available at Summary: Students learning the processes of addition and subtraction need a rich problem solving and problem-posing environment that should include: 1. Experiences with addition and subtraction in both in-school and out-ofschool situations to gain a broad meaning of the symbols +/. 2. Experiences both posing and solving a broad range of problems. 3. Experiences using their contextual meaning of +/ to solve and interpret arithmetic problems without a context. 4. Experiences using solution procedures that they conceptually understand and can explain. Summary: Meaningful instruction and drill go together as part of a successful learning experience, but meaningful instruction must precede drill or practice (Dessert). A balanced approach to both is needed in mathematics classrooms, as students who can access both memorized and meaningful ideas in mathematics achieve at a higher level than those who rely on either one without the other. (Askew and William, p. 47) Summary: Teachers need to choose instructional activities that integrate everyday uses of mathematics into the classroom learning process as they improve students interest and performance in mathematics. (Fong, Krantz, and Nisbett, p. 38) References Askey, M. and William, D. Recent Research in Mathmatics Education London. Her Majesty s Stationary Office, Fong, G., Krantz, D., and Nisbett, R. The Effects of Statistical Training on Thinking About Everyday Problems. Cognitive Psychology, 1986, 18: HANDOUT 13 (continued) Helping with Math at Home: Ideas for Parents

17 Handout 14 Feedback Form Session Title: Location: Date: 1. What new ideas do you have as a result of this session? 2. What ideas from this session will you use with your child(ren)? 3. Overall, how would you rate this session? Not Informative Extremely Informative 4. Is there anything else you would like us to know? 5. Would you like to be informed about any upcoming sessions? If so, please provide the following: Name: Address: Helping with Math at Home: Ideas for Parents HANDOUT 14