Why math instruction has changed!

Editor's Notes

• #2: Some of the myths that directed mathematics instruction in the past have been replaced with research on how children learn mathematics. This research has indicated that the teaching of mathematics must change from some of the “traditional” methods that we experienced as students when we went to school.
• #3: Everyone can do math , even though participants may have experienced math instruction in the past that made it appear that only a few students could be good at math. More inclusive instructional and assessment strategies and materials allow all students to learn math, though not in the same way, not to the same depth of understanding, and not in the same amount of time.
• #4: Many adults grow up with the idea that some students are good at math and others aren ’ t and that there is nothing that can be done about it. But, we know that all students can learn math skills, just like all students can learn to read or write. It is important for us to keep a positive attitude about our choices and ability to succeed in math. Too often, society has accepted the stereotype that mathematics is for the few, not the many. It is time to dispel the myth that mathematics is for some and to demand mathematics success for all.
• #6: Mathematics no longer takes place only in the classroom. Mathematics is everywhere. To reach their full potential in the twenty-first century students need to have an understanding of mathematics. Mathematics skills are for everyday life. Mathematical skills required to function in today ’ s world include the ability to: - set up problems - use a variety of techniques to solve problems - work with others to solve problems - apply mathematical concepts to complex problems.
• #7: Math is a subset of literacy, rather than literacy and mathematics being two independent sets.
• #8: Mathematical literacy involves more than executing procedures. It implies a knowledge base and the competence and confidence to apply this knowledge in the practical world. A mathematically literate person can estimate, interpret data, solve day-to-day problems, reason in numerical, graphical, and geometric situations, and communicate using mathematics. Mathematical literacy is necessary both at work and in daily life. It is one of the keys to functioning in a changing society.
• #9: Research about how children learn shows that if they cannot talk about their learning, they do not own it. Marilyn Burns (1995) uses the phrase “inking your thinking,” observing that when students write their thinking, they sort, clarify, and refine their ideas.
• #11: Math requires both creativity and mastery of facts and procedures. People need to know that 1+1=2, but more importantly they need to know when to add. Students engage in problem solving in all strands of the mathematics curriculum. Students should use problem-solving methods extensively as a means of developing the full range of mathematical skills and knowledge in all strands.
• #12: Few people question the belief that all learners construct their own understanding based on a variety of experiences. People do not necessarily believe something just because somebody in authority says it is true. Most people learn best when they are active participants, rather than passive observers, of the learning process. Therefore, the variety and quality of mathematical experiences selected by teachers is crucial.
• #13: In some classrooms, the teacher presents the students with information and the students copy notes and begin homework. The students ’ role in this exercise is largely passive. They are to accept what they are told and attempt to master each new rule. Students need to be in a classroom where they are “ doing ” mathematics. When students are engaged in activities in which they explore, investigate, solve, justify, discover, construct, predict, it is impossible for them to be passive observers.
• #16: As the teaching of mathematics has changed, so have the assessment practices. Chapter-end tests are simply inadequate in a student-centered, problem-oriented classroom.
• #17: .
• #18: Research indicates that calculators do not hinder arithmetic skill development, but in fact enhance it, when used appropriately. Many parents worry that their children will not learn their basic math facts if allowed to use calculators. Research indicates that how calculators are used is the critical factor. When calculators are used in a variety of appropriate ways, students perform as well or better on computational skills than those who use paper-and-pencil methods.
• #19: Mathematics educators have long realized that the use of something ‘concrete’ should not stop once a person reaches a certain age. For some mathematical tasks, many university students are operating at Piaget’s concrete level of understanding. It is important that students can make connections between abstract symbolism and every day life, rather than considering this level of thinking less mature. Teachers should use the phrase: “ Use manipulatives if you want.” rather than “Use manipulatives if you need.”