Math Makes SenseParent Night

Jeannie DeBoice Numeracy Curriculum Advisorjdeboice@sd62.bc.ca 474-9851

What is Numeracy? Math is the science of pattern and orderEveryday 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 dont knowcan use reasoning and evidence to prove a pointcan explain what they are doing as they work with numbers, symbols, and geometric objectsknow which processes to use to solve problems and can tell why can talk about their ideas and show their thinkingNumerate individuals not only know mathematics, but also understand it in personally meaningful terms.-BC Numeracy Performance Standards

Math: It Doesnt Have To be a Four-Letter WordAsk anyone what their least favourite subject was in school and chances are theyll 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 irrelevantWe 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 meaningchildren must create meaning themselvesClassroom 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.

How is this approach different?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 KappanWhen we simply learn the rules, they can be easily forgotten- or misused. John Van de Walle

Now, create a story problem to go with your equation.1 = ?

Fractions in the Math Makes Sense ClassroomMany children & adults can solve this using a rule (invert & multiply) quickly the intent of an algorithmBut most people cant 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 1 meters of ribbon how many meter lengths can you get from it?

rulescan be easily forgotten or misused. Theres an enormous difference between memorizing a few key facts and having an authentic grasp of the materialThe emphasis on memorizing trivia, names, facts and formulas must stop. Its poor use of precious educational time. from Brain-Based Learning, p. 185 by Eric Jensen

Learners Learning to Create Their Own MeaningAuthors 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 learners 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

Theres 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 SaundryWhat will you do with the remainder that makes sense?

1980s Approach to Mathematics 1. Mathematics is associated with certainty2. Knowing mathematics means being able to get the right answerCommon Beliefs:QUICKLY!

Teacher Facilitated SharingFundamental Beliefs:

Mathematics is about making sense Sense-Making Approach to Mathematics2. Students must come to believethat they can make sense of mathematics

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 themDelay! 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 misconceptionspresent their ideas, feel valued and feel safe to express themgain insight from others perspectives.develop a mathematics vocabulary

Math Everywhere!- from Math For FamiliesPlay games together like board games, card games or dice games. Talk about what makes the games fun/challengingTalk 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.

More Math Everywhere!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!

Math Websites for you & Your ChildMath games on the computer are most successful when played with a parent present to talk about concepts and verbalize thinking.

www.AchieveBC.cawww.kidsdomain.com/games/math2.htmlwww.eduplace.com/math/brainwww.Mathstories.com

Math is the science of pattern and order. There are lots of ideas to learn and some of these are basic skills which are as important to know well. But mastery of basic skills is no more doing mathematics than playing scales on the piano is making music. (Van de Walle) Drill should never come before understanding.The most basic idea in Numeracy is that mathematics should make sense!Student must believe that they are capable of making sense of math.Numeracy is one of the 9 essential skills identified by Human Resources Development Canada.The underpinnings of everyday life are increasingly mathematical and technological.Numeracy is making sense of math and believing we can do math. A numerate person doesnt see math as a series of arbitrary rules, but as a science of making sense of number patterns and relationships.Numeracy is the ability to make sense of math and to use it effectively in real life situations.Numerate people:- can use what they know to figure out what they dont 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 thinkingNumerate people can explain what they are doing as they work with numbers and symbols. p. 13(from Math For Families Achieve BC)www.AchieveBC.ca Math For Families: Helping Your Child With Math at Home How did this program come about? What does research say about teaching math? Mathematics is one of humanitys great achievements. By enhancing the capabilities of the human mind, mathematics has facilitated the development of science, technology, engineering, business, and government. For people to participate fully in society, they must know basic mathematics. Citizens who cannot reason mathematically are cut off from whole realms of human endeavor. The mathematics students need to learn today is not the same mathematics that their parents and grandparents needed to learn. All young [Canadians] must learn too think mathematically, and they must think mathematically to learn. P. 1, Adding It Up Curricular reform is moving across North America, and Canada is part of this movement to raise achievement levels. This has come about as a result of a need for our children to compete in a highly competitive global economy. As in Language Arts, the shift in math is away from memorizing facts and rules to understanding the whole meaning of ideas and procedures. This reform has also evolved form constuctivism learning theory, which states children must create meaning themselves, not be expected to simply memorize rules. Learning involves a complex series of external and internal events that result in the creation of mental connections. The teachers role is to facilitate the students own cognitive processes by carefully selecting tasks that elicit thinking just beyond the students current state of knowledge. Classroom instruction can stimulate learning by relating new materials to old and by using oral and written activities to help students make intellectual connections among new ideas. (p. 28, Pearson research)

How is this math program and approach different? Van de Walle defines conceptual knowledge of mathematics as logically interconnected ideas developed over time. Students and teachers who have a conceptual understanding of mathematics truly understand it they have more than just a grasp of its facts, rules, and procedures. (p. 30, Pearson)New ideas are connected to old thats what contemporary research tells us. Things we learn with understanding, that we can connect to something we already know, is easily recalled and used in various situations. Think of your own learning! Learning this way allows children to solve unfamiliar problems, and to spot and correct errors theyve made in problem solving. However, when we simply learn the rules, they can be easily forgotten or misused. (show example)

Why write in Math? Why all these questions asking children to explain their thinking?Funny, we dont question the need for writing and reasoning in other subjects we all wrote observation, predictions and conclusions in Science class, essays explaining our understanding of events in Social Studiesbut somehow writing in Math seems odd!However, our students are not at this time very able when it comes to non-fiction reading and writing.Students need to read to know , talk to explain and write to communicate not just in writing class!

Traditionally, discussion has not been a part of mathematics class; now it is centre stage.Successfully communicating about mathematics is part of the process of learning mathematics.Why?- it helps students organize and reflect on their own mathematical thinking. When theyre asked to describe the steps they took to solve a problem, they are encouraged to think out loud in an organized way. It helps clarify and resolve misconceptions.- Student present their ideas and feel valued and that it is safe to express them. They also gain insight from others perspectives.- student benefit when talking mathematics in the classroom is valued and routine.- teachers model mathematical thinking by thinking out loud.- students develop a mathematics vocabulary which is also part of being able to communicate ideas precisely.