M athematics standards

1. Mathematics standards MATH 123

2. New math • When the Soviets launched Sputnik 1 in 1957, concerns emerged that the United States was falling behind in the areas of math and science. As a consequence, “New Math” was created in the 1960s. The emphasis of this New Math was on set language and properties, proof, and abstraction. Now a butt of many jokes, the New Math was confusing to many, and left many children behind. This brought about the trend of Back to Basics in the late 1970s and early 1980s. The pendulum is still swinging between back to the basics and inquiry approaches to teaching mathematics. http://www.education.com/reference/article/history-mathematics-education-NCTM/

3. “A Nation at Risk” • “Our Nation is at risk. Our once unchallenged preeminence in commerce, industry, science, and technological innovation is being overtaken by competitors throughout the world. … We report to the American people that while we can take justifiable pride in what our schools and colleges have historically accomplished and contributed to the United States and the well-being of its people, the educational foundations of our society are presently being eroded by a rising tide of mediocrity that threatens our very future as a Nation and a people. What was unimaginable a generation ago has begun to occur--others are matching and surpassing our educational attainments.” (National Commission for Excellence in Education, 1983) • You can find the full report at http://www2.ed.gov/pubs/NatAtRisk/risk.html

4. At risk? • Since the publication of the report, the U.S. educational system has been consistently vilified by many. • The report claims, “The College Board's Scholastic Aptitude Tests (SAT) demonstrate a virtually unbroken decline from 1963 to 1980. Average verbal scores fell over 50 points and average mathematics scores dropped nearly 40 points.” • These are serious accusations.

5. But are they true? • Well, not quite. There was some bad mathematics involved in this research. • This was uncovered by the Sandia report, which was never given much attention. • Instead of catastrophic decline, they found “steady or slightly improving trends“ on “nearly every measure” • For example, although the SAT averages did indeed drop, they increased in nearly every category, in terms of performance, socioeconomic status, and ethnicity. • How is this possible? Simple: as the numbers of minority students taking the SAT increased, the averages changed.

6. Therefore… • The lower SAT averages are actually a consequence of increased access to education, a goal that “A Nation at Risk” strongly promotes. • In other words, “A Nation at Risk” may not be completely reliable. • Yet it changed education in the U.S. significantly. The endless cycle of increasing assessments, including the No Child Left Behind legislation began here.

7. NCTM Standards • In 1989 the National Council of Teachers of Mathematics (NCTM) released the Curriculum and Evaluation Standards for School Mathematics, and in 2000 the Principles and Standards for School Mathematics. These publications stress problem solving, communication, connections, and reasoning. NCTM Standards state that “the study of mathematics should emphasize reasoning so that students can believe that mathematics makes sense” (NCTM, 1989, p. 29). • One of the NCTM principles is that equity, stating that all students should have equal access to high quality mathematics instruction. This has not been the case in the United States. • http://www.education.com/reference/article/history-mathematics-education-NCTM/?page=2

8. NCTM standards: overview “We live in a time of extraordinary and accelerating change. New knowledge, tools, and ways of doing and communicating mathematics continue to emerge and evolve. The need to understand and be able to use mathematics in everyday life and in the workplace has never been greater and will continue to increase. In this changing world, those who understand and can do mathematics will have significantly enhanced opportunities and options for shaping their futures. Mathematical competence opens doors to productive futures. A lack of mathematical competence keeps those doors closed. The National Council of Teachers of Mathematics (NCTM) challenges the notion that mathematics is for only the select few. On the contrary, everyone needs to understand mathematics. All students should have the opportunity and the support necessary to learn significant mathematics with depth and understanding. There is no conflict between equity and excellence.”

9. Math wars • The Math wars are an ongoing debate (or battle?) between proponents of inquiry-based learning, and proponents of bask to the basics approach to teaching and learning mathematics. The debate was triggered by the publication of 1989 NCTM Standards, and has especially been heated in California and Washington. • Proponents of the back to the basics approach argue that children need to learn, memorize, and practice the basic facts before they are able to start thinking about more abstract ideas. In other words, children are first taught the standard algorithm for addition, and then required to think about properties of addition, or why the algorithm works. • Inquiry based learning is the opposite. Students first develop their own conceptual understanding of addition, and only then learn the standard algorithm. Conceptual understanding is a primary goal and algorithmic fluency is expected to follow secondarily. • A considerable body of research by mathematics educators has generally supported reform mathematics and has shown that children who focus on developing a deep conceptual understanding (rather than spending most of their time drilling algorithms) develop both fluency in calculations and conceptual understanding.

10. About the Common Core Standards • The Common Core State Standards in Mathematics are the first set of mathematics standards to be adapted (almost) nationwide. They describe knowledge and skills that mathematics learners need to acquire, but they do not proscribe how these skills will be attained: they are standards, not a curriculum. • The standards focus on college readiness and attempt to make the mathematics content covered deeper but narrower. • The standards have been controversial for a number of reasons. They are currently in place in 43 states. Alaska and Texas never intended to adapt them, while other states have dropped out in the process. • A video about the standards

11. Common Core in Washington • Washington State has started implementing CCSM in 2013-2014. Starting in 2014, the transition to the new standards is complete and students are tested according to the new standards. • The standards require a major shift in teaching, as they, like the NCTM standards, require conceptual understanding rather than just procedural competency.

12. Common Core Standards for mathematical practice 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. full text here

13. Common Core content standards • We will be talking about these throughout the semester. The course will be closely aligned with the standards and you will have a chance to read and respond to them.