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Math Makes SenseParent Night Jeannie DeBoice Numeracy Curriculum Advisor firstname.lastname@example.org 474-9851
What is Numeracy? • Math is the science of pattern and order • Everyday life is increasingly mathematical and technological. • Most basic idea in Numeracy: mathematics should make sense! Mastery of basic skills “… is no more ‘doing mathematics’ than playing scales on the piano is making music.” (Van de Walle)
Numerate people... • can use what they know to figure out what they don’t know • can use reasoning and evidence to prove a point • can explain what they are doing as they work with numbers, symbols, and geometric objects • know which processes to use to solve problems and can tell why • can talk about their ideas and show their thinking ‘Numerate individuals not only “know” mathematics, but also understand it in personally meaningful terms.’ -BC Numeracy Performance Standards
Math: It Doesn’t Have To be a Four-Letter Word • “Ask anyone what their least favourite subject was in school and chances are they’ll tell you it was math. The anxiety around finding the one right answer and doing it quickly disenfranchised so many learners that people simply believed themselves incapable of understanding mathematics. Rigid teaching methods – a quick demo of the procedure of the day, followed by pages of practice – made math incomprehensible to most children, or at best boring and irrelevant…We are learning to re-imagine math classrooms as places where students of all abilities work together on the same problem: a rich task focused on a concept worth revisiting over time.” - Carole Saundry, “Student Diversity” 2006
What does the research say? • the shift is away from memorizing facts and ‘rules’ to understanding the whole meaning • children must create meaning themselves • Classroom instruction relates new materials to old by using oral and written activities “All young Canadians must learn to think mathematically, and they must think mathematically to learn.”
“The bottom line is that research has shown that things our brain does not understand are more likely to be forgotten. It is part of our makeup.”-John Marshall, p. 362 Phi Delta Kappan “When we simply learn the rules, they can be easily forgotten- or misused.” – John Van de Walle How is this approach different? 1¾ ÷ ½ = ? Now, create a story problem to go with your equation.
Fractions in the Math Makes Sense Classroom • Many children & adults can solve this using a ‘rule’ (invert & multiply) quickly – the intent of an algorithm • But most people can’t explain how or why it works. • We teach children the concept of division in fractions so they can apply it in a context: • Algorithms can be useful, but can also steer us away from simple solutions! You have 1¾ meters of ribbon – how many ½ meter lengths can you get from it?
“…rules…can be easily forgotten – or misused.” • “There’s an enormous difference between memorizing a few key facts and having an authentic grasp of the material…The emphasis on memorizing trivia, names, facts and formulas must stop. It’s poor use of precious educational time.” fromBrain-Based Learning, p. 185by Eric Jensen
Learners Learning to Create Their Own Meaning • “Authors Brooks and Brooks remind us there is no meaning in textbooks. There is no meaning from the presenter. There is only meaning from within. They make a persuasive point for the use of constructivist classrooms. The fundamentals of this approach are very brain-based. They encourage the use of integrated thematic learning. They encourage the use of learner’s prior knowledge. They build thinking skills and confidence in learners. How?...
How? • Two key strategies: • First, they operate out of the context that learners have to learn to create meaning for themselves in what they learn. • Second, this is done through problems, questions and projects that challenge the learners. Once again, the genius of this process is that the presenter gets out of the way of the learner so that the learner can creates, from scratch, real meaning in the learning.” - Eric Jensen, Brain-Based Learning, p. 196
There’s more than one right way….. • “If we ask ‘What is 380 ÷15?’ there is only one right answer – 25 remainder 5, or 25.3333 – and one assumed right method. Some students will find the answer effortlessly and be ready for another question quickly, while some will struggle with the algorithm, perhaps arriving at the right answer even without fully understanding the question or the processes involved. • If we instead ask, ‘How can you show 380 divided into 15 groups? How many different ways can you find?’ “ –Carole Saundry • What will you do with the remainder that makes sense?
Teacher Directed Lesson Practise Problem Solving Application • 1980’sApproach • to Mathematics Common Beliefs: 2. Knowing mathematics means being able to “get the right answer… 1. Mathematics is associated with certainty QUICKLY!
Problem Solving Scenario Teacher Directed Lesson Activity& Conversation Practise Problem Solving Application Clarify - Refine - Practise - Apply • Sense-Making Approach • to Mathematics • Fundamental • Beliefs: • Mathematics is • about making • sense 2. Students must come to believe that they can make sense of mathematics Teacher Facilitated Sharing
Traditional Algorithms • It is not that the traditional algorithms cannot be taught with a strong conceptual basis…. The problem is that the traditional algorithms, especially for addition and subtraction, are not natural methods for students. • As a result, the explanations generally fall on deaf ears. Far too many students learn them as meaningless procedures, develop error patterns, and require an excessive amount of reteaching or remedation. • If you are going to teach them…Delay! The understanding that children gain from working with invented strategies will make it easier for you to teach the traditional methods. - John Van de Walle, p. 162
Benefits of Personal Strategies • Base-ten concepts are enhanced. • Students make fewer errors. • Less reteaching is required. • Personal strategies provide the basis for mental computation and estimation.
Why write in Math? • When you add language to math concepts, you own them. • Students need to ‘read to know’ , ‘talk to explain’ and ‘write to communicate’ – not just in writing class! • “When reading and writing skills are used in a real world context such as science and math, they become meaningful to the student.”
Why have discussions in Math? So students can: • organize and reflect on their own mathematical thinking • clarify and resolve misconceptions • present their ideas, feel valued and feel safe to express them • gain insight from other’s perspectives. • develop a mathematics vocabulary
Play games together like board games, card games or dice games. Talk about what makes the games fun/challenging Talk about Math, encouraging your child to explain his/her thinking, sequence & count, compare, use logical thinking, describe the world. Talk about Math as you show your child how you use math in your life, such as measuring for recipes, estimating amounts of paint or wallpaper, use the clock to plan, read schedules. Math Everywhere!- from Math For Families
Promote Math as Thinking, not Memorization: Some math needs to become automatic, but right now your child needs time for thinking and reasoning. Ask your child to explain how he/she figured things out: “How did you know that?” Value their thinking! Keep in mind memorizing does not always mean understanding and that math is about making sense. Model Positive Attitudes Towards Math: Have fun together while doing math-related activities such as measuring ingredients, counting dishes for table setting, sorting laundry, building projects. Model the old saying: “Try, try again!” – say, “Can you think of another way to put the shapes together?” Spend time talking about your positive math experiences – kids are influenced by the attitudes of the adults around them! More Math Everywhere!
Math Websites for you & Your Child Math games on the computer are most successful when played with a parent present to talk about concepts and verbalize thinking. • www.AchieveBC.ca • www.kidsdomain.com/games/math2.html • www.eduplace.com/math/brain • www.Mathstories.com