ADDING IT ALL UP: MATHEMATICS FOR THE 21 ST CENTURY LEARNER

1. ADDING IT ALL UP: MATHEMATICS FOR THE 21ST CENTURY LEARNER Presented by Carollee Norris Numeracy Support Teacher, School District #60 Peace River North cnorris@prn.bc.ca blog: focusonmath.wordpress.com

2. WHAT HAPPENED TO MATH? • When did it start changing? • Why is it changing? • How is it changing?

3. WHAT DOES A 21ST CENTURY LEARNER NEED TO KNOW AND BE ABLE TO DO? Things such as…. • The “basics” • Critical thinking skills • Problem solving skills

4. UNIVERSAL DESIGN:WHAT IS IT? • Ron Mace, creator of the concept, defined it as “…the design of products and environments to be usable by all people, to the greatest extent possible, without the need of adaptation or specialized design.” • The idea is to plan for the people you will serve from the beginning. Don’t adapt later. • Examples: curb cuts and closed-captioned TV

5. UNIVERSAL DESIGN FOR LEARNING:WHAT DOES IT LOOK LIKE IN EDUCATION? • UDL was first developed in the 1990s by researchers at the Center for Applied Special Technology (CAST). They define UDL as this: “…a research-based framework for designing curricula (educational goals, methods, materials and assessments) that enable all individuals to gain knowledge, skills and enthusiasm for learning.

6. UNIVERSAL DESIGN FOR LEARNING:ADDRESSING THE DIFFERENCES

7. UNIVERSAL DESIGN FOR LEARNING:“FINGERPRINTS” IN THE BRAIN • The CAST researchers discovered that everyone – non-disabled and disabled alike – exhibits differences in the way each of these networks function. It turns out that the activity in these networks is actually as unique as each person’s fingerprints. And that means that there is no such thing as a “typical learner” and that any kind of “one-size-fits-all” educational approach does not reach all learners. (bolding by CN)

8. “MATHEMATICS IS A SCIENCE OF PATTERN AND ORDER.” Everybody Counts Mathematical Sciences Education Board, 1989, p.31

9. “KNOWING MATHEMATICS IS DOING MATHEMATICS.”NCTM CURRICULUM AND EVALUATION STANDARDS FOR SCHOOL MATHEMATICS, 1989 • What are the verbs we associate with doing science?

10. “KNOWING MATHEMATICS IS DOING MATHEMATICS.”NCTM CURRICULUM AND EVALUATION STANDARDS FOR SCHOOL MATHEMATICS, 1989 • explore • investigate • conjecture • solve • justify • represent • formulate • discover • construct • verify • explain • predict • develop • describe • use • discuss

11. A farmer has 28 sheep in his pasture by the pond and 39 sheep in his pasture beyond the barn. How many sheep does the farmer have? How many different strategies can you use to solve the problem?

12. THE PROCESSES OF MATHEMATICS • Communication • Connections • Mental Math and Estimation • Problem Solving • Reasoning • Technology • Visualization Every math learning outcome K-12 is linked to specific processes. From the BC Mathematics K-12 curricular documents (IRP’s)

13. VISUALIZATION: POSSIBLE TOOLS • ten frames • 100 charts • geoboards • square tiles • pattern blocks • algebra tiles • two-colour counters • fraction circles • dot cards • dice • dominoes • fraction strips • percent grids • 100 dot arrays

14. “Understanding ‘lives’ in the processes”. C. Norris et al, 2012.

15. THESE IDEAS ARE FOSTERED ALL TOO OFTEN IN THE “TYPICAL” CLASSROOM: • DOING MATH means following the rules laid down by the teacher. • KNOWING MATH means remembering and applying the correct rule when the teacher asks a question. • CORRECTNESS is determined by checking with the teacher or the answer key.

16. GOOD MATHEMATICS IS NOT HOW MANY ANSWERS YOU KNOW… but how you behave when you don’t know. Author unknown

17. “A typical classroom narrows our thinking strategies and answer options. The teacher insisting on a ‘right answer’ is not healthy for growing a smart, adaptive brain. Good quality education education encourages the exploration of alternative thinking, multiple answers, and creative insights.” Jensen, 1998, p.16.

18. “No matter how lucidly and patiently teachers explain to their students, they cannot understand for their students.” Schifter & Cathy Fosnot, 1993

19. “Knowledge is the hard-won, somewhat tentative fruit of many attempts to understand through the constant pondering, testing, and rethinking of ideas”. Wiggins & McTighe, 1999

20. WHAT DOES MATH LOOK LIKE IN YOUR CLASSROOMS, YOUR SCHOOLS, YOUR DISTRICT? • Can you see the processes (those linked to every learning outcome) taking place? • communication, connections, mental math & estimation, problem solving, reasoning, technology, visualization • Are students making meaning of math? Can students demonstrate an understanding of concepts? • Are multiple strategies being sought and used?

21. HOW DO WE SUPPORT MATH CHANGES IN OUR DISTRICTS? • Look at the most important elements in the change process: • Readiness to change – Does the teacher have the resources and knowledge to successfully make a lasting change? • Barriers to change - Is there anything preventing the teacher from changing? • Expect relapse - What might trigger a return to a former behavior? • What can you put in place to support the process?

22. REFERENCES • Everybody Counts, Mathematical Sciences Education Board, 1989. • Jensen, Eric. Teaching With the Brain in Mind. ASCD, 1998. • Lappan, G & D. Briars, “How Should Mathematics Be Taught”, Prospects for School Mathematics. NCTM, 1995 • Norris C., S. Chorney, D. Wright, & T. Thielmann. “Communication on Communication”. Vector, Volume 53, Issue 1 (Spring 2012).

23. REFERENCES • Schifter, D. & C. Fosnot, “Reconstructing Mathematics Education: Stories of Teachers Meeting the Challenge of Reform”, Teachers College Press, 1993. • UDL information from • http://marylandlearninglinks.org/1020 • Van de Walle, J. & S. Folk. Elementary and Middle School Mathematics: Teaching Developmentally (Canadian Edition). Pearson, 2005. • Wiggins, G & J. McTighe. Understanding by Design. ASCD, 2005.