Research Proven Strategies in Mathematics An Access Center Presentation to the Information Sharing Communities A Pre

2. Historical Perspectives: Math was taught as a set of facts, rules, and procedures Recent reforms triggered the development of Curriculum and Evaluation Standards for School Mathematics (NCTM 1989, 1991,1995) Revised standards became known as Principles and Standards for School Mathematics (NCTM, 2000) Identified six overarching principles Historically, Math was taught as a set of facts, rules, and procedures for dealing with numbers and quantitative concepts. More recently, reform efforts initiated the development of standards. These standards were developed by the National Council of Teachers of Mathematics. First in 1989 and as of 2000 are now revised and called Principles and Standards for School Mathematics These standards were created to ensure that students are able to solve complex problems rather than to reiterate rote-memorized facts. This recent revision provides us with 6 overarching principles to describe features of high-quality math education. And include equity, curriculum, teaching, learning, assessment, and technology. Historically, Math was taught as a set of facts, rules, and procedures for dealing with numbers and quantitative concepts. More recently, reform efforts initiated the development of standards. These standards were developed by the National Council of Teachers of Mathematics. First in 1989 and as of 2000 are now revised and called Principles and Standards for School Mathematics These standards were created to ensure that students are able to solve complex problems rather than to reiterate rote-memorized facts. This recent revision provides us with 6 overarching principles to describe features of high-quality math education. And include equity, curriculum, teaching, learning, assessment, and technology.

3. Current NCTM Standards (K-12): Number and Operations Algebra Geometry Measurement Data Analysis and Probability Problem Solving Reasoning and Proof Communication Connections Representations In addition to the 6 principles there are standards in each of the categories listed on the screen. For example, the Number and Operations Standard states that all students must understand numbers, understand meaning, and compute fluently.�Specific expectations within this standard vary according to grade level. Most standards require an �authentic� application of knowledge in solving real-life problems or creating real-life tasks.In addition to the 6 principles there are standards in each of the categories listed on the screen. For example, the Number and Operations Standard states that all students must understand numbers, understand meaning, and compute fluently.�Specific expectations within this standard vary according to grade level. Most standards require an �authentic� application of knowledge in solving real-life problems or creating real-life tasks.

4. How do these standards relate to Access? No information on how to address individual needs of students with disabilities The 2000 Principles & Standards briefly addresses students with disabilities in their Equity Principle (p. 11) However, according to Maccini & Gagnon (2002), many special and general educators are not aware of the NCTM standards Despite the significant effects the NCTM standards have had on math education, the 1989 NCTM standards made no direct reference to students with Disabilities. The equity principle states, �All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study � and support to learn � mathematics. Equity does not mean that every students should receive identical instruction; instead , it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students.Despite the significant effects the NCTM standards have had on math education, the 1989 NCTM standards made no direct reference to students with Disabilities. The equity principle states, �All students, regardless of their personal characteristics, backgrounds, or physical challenges, must have opportunities to study � and support to learn � mathematics. Equity does not mean that every students should receive identical instruction; instead , it demands that reasonable and appropriate accommodations be made as needed to promote access and attainment for all students.

5. Suggestions from research : According to Carnine (1998), five major components are required for effective mathematics instruction. These include: Focus on �big ideas� Teach �conspicuous� strategies (neither too broad or too specific) (see also Montague, 1998). Guidelines written by the NCTM, also support this focus on �big ideas�� They suggest that, �foundational ideas like place value, equivalence, proportionality, function, and rate of change should have prominent place in the mathematics curriculum because they enable students to understand other mathematical ideas and connect ideas across different areas of mathematics�. (p.15). Math standards reflect new theories and research about how children learn & has placed an increased emphasis on applied problem solving and �authentic� knowledge. Children are taking more active roles in the classroom thus are gaining a deeper understanding of topics. Many textbooks are not designed using the concept of big ideas. . For example, in most textbooks . . .see next slideGuidelines written by the NCTM, also support this focus on �big ideas�� They suggest that, �foundational ideas like place value, equivalence, proportionality, function, and rate of change should have prominent place in the mathematics curriculum because they enable students to understand other mathematical ideas and connect ideas across different areas of mathematics�. (p.15). Math standards reflect new theories and research about how children learn & has placed an increased emphasis on applied problem solving and �authentic� knowledge. Children are taking more active roles in the classroom thus are gaining a deeper understanding of topics. Many textbooks are not designed using the concept of big ideas. . For example, in most textbooks . . .see next slide

6. For example For example, in most textbooks students are expected to learn different formulas to calculate the volume of seven 3 dimensional figures ( rectangular prism, wedge, cylinder, cone, etc). �This strategy emphasizes rote memorization rather than big ideas. In actuality, if a student understands the �big idea� behind 3-dimensional volume. . .all seven formulas turn out to be variations of one (more simple formula) That is. . . The area of the base times the height. For example, in most textbooks students are expected to learn different formulas to calculate the volume of seven 3 dimensional figures ( rectangular prism, wedge, cylinder, cone, etc). �This strategy emphasizes rote memorization rather than big ideas. In actuality, if a student understands the �big idea� behind 3-dimensional volume. . .all seven formulas turn out to be variations of one (more simple formula) That is. . . The area of the base times the height.

7. Suggestions from research (cont): Make efficient use of time on prioritized objectives. Communicate strategies in a clear, explicit manner. Provide practice and review to promote retention (Mastropieri & Scruggs, 2004; Harniss, Stein, & Carnine, 2000). Research conducted by Schmidt, McKnight, and Raizen (1997) compared math and science curricula around the world. They analyzed textbooks and curriculum guides from the countries that participated in the Third International Mathematics and Science Study (TIMSS). They found that in the U.S. math and science curricula cover more topics by ninth grade than 50 to 75 percent of other countries and that new topics (skills, concepts, & so on) are added each year. Most other countries teach fewer concepts or topics each year, and they teach the content to mastery. Standards are important because they determine �what� teachers are expected to teach at specific grade levels. Increasingly, they also are defining �how� teachers should teach the content. While the primary purposes of the standards are to Focus the general education curriculum on a core of important and challenging content, and Ensure that every student in a state or district receives instruction in the same challenging content. Therefore, it is important for educators to be clear & explicit in their instruction. Finally, access requires that students with disabilities be provided with the supports necessary to allow them to benefit from instruction. This requirement applies across all instructional domains & Amanda will touch more on this later when she addresses strategies and alignment of IEPs. Research conducted by Schmidt, McKnight, and Raizen (1997) compared math and science curricula around the world. They analyzed textbooks and curriculum guides from the countries that participated in the Third International Mathematics and Science Study (TIMSS). They found that in the U.S. math and science curricula cover more topics by ninth grade than 50 to 75 percent of other countries and that new topics (skills, concepts, & so on) are added each year. Most other countries teach fewer concepts or topics each year, and they teach the content to mastery. Standards are important because they determine �what� teachers are expected to teach at specific grade levels. Increasingly, they also are defining �how� teachers should teach the content. While the primary purposes of the standards are to Focus the general education curriculum on a core of important and challenging content, and Ensure that every student in a state or district receives instruction in the same challenging content. Therefore, it is important for educators to be clear & explicit in their instruction. Finally, access requires that students with disabilities be provided with the supports necessary to allow them to benefit from instruction. This requirement applies across all instructional domains & Amanda will touch more on this later when she addresses strategies and alignment of IEPs.

8. Other evidence-based strategies(Not specific to mathematics instruction) Cooperative Learning, Mnemonic Instruction, Class Wide Peer Tutoring, and Direct Instruction (Harniss, Stein, & Carnine, 2000).

9. Resources What Works Clearinghouse http://www.w-w-c.org National Council for Teachers of Mathematics http://www.nctm.org The Access Center http://www.k8accesscenter.org

10. Concluding Thoughts According to the National Research Council (1989): Mathematics is the key to opportunity. No longer just the language of science, mathematics now contributes in direct and fundamental ways to business, finance, health, and defense. For students, it opens doors to careers. For citizens, it enables informed decisions. For nations, it provides knowledge to compete in a technological economy. To participate fully in the world of the future, America must tap the power of mathematics (p.1).

11. This content was developed by staff at The Access Center: Improving Outcomes for All Students K-8, funded by U. S. Department of Education, Office of Special Education Programs and housed at the American Institutes for Research. Retrieved [today's date], from the World Wide Web: http://www.k8accesscenter.org