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Introduction to Numeracy What is numeracy ? How is it related to mathematics?

Introduction to Numeracy What is numeracy ? How is it related to mathematics? Why is numeracy important?. What Is Numeracy Are there levels of numeracy? (Nature and limits) Where does it come from? (How is it taught/nurtured, supported?)

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Introduction to Numeracy What is numeracy ? How is it related to mathematics?

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  1. Introduction to Numeracy What is numeracy? How is it related to mathematics? Why is numeracy important?

  2. What Is Numeracy Are there levels of numeracy? (Nature and limits) Where does it come from? (How is it taught/nurtured, supported?) The roles of attitudes, anxiety, and attributions in one’s own development as a numerate individual

  3. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdfhttp://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

  4. “The eminence, safety, and well-being of nations have been entwined for centuries with the ability of their people to deal with sophisticated quantitative ideas. Leading societies have commanded mathematical skills that have brought them advantages in medicine and health, in technology and commerce, in navigation and exploration, in defense and finance, and in the ability to understand past failures and to forecast future developments. History is full of examples.” National Mathematics Advisory Panel (2008) p. xi

  5. School Readiness and Later Achievement: “ …the strongest predictors of later achievement are school-entry math, reading, and attention skills. … early math skills have the greatest predictive power, followed by reading and then attention skills. …, even among children with relatively high levels of problem behavior. …for boys and girls and for children from high and low socioeconomic backgrounds.” Duncan et al., Developmental Psychology (2007).

  6. What Is Numeracy? Richard Barwell (2004) For the Learning of Mathematics Vol. 24, pp. 20-22 Historical context of use of “numeracy” emerged largely in the field of “literacy.” Quoting Baker, 2003:

  7. What Is Numeracy? Richard Barwell (2004) For the Learning of Mathematics Vol. 24, pp. 20-22 Historical context of use of “numeracy” emerged largely in the field of “literacy.” Quoting Baker, 2003: “Numeracy events – occasions in which numeracy activity is integral to interactions and interpretative processes…”

  8. What is numeracy? Merriam-Webster: “the capacity for quantitative thought and expression”

  9. What is numeracy? Merriam-Webster: “the capacity for quantitative thought and expression” OED: “… ability with or knowledge of numbers”

  10. What is numeracy? • “Student numeracy refers to the ability of students to identify and understand the role that mathematics plays in the world. … to use mathematics in ways that meet the needs in living and working….” • Human Resources and Skills Development Canada www.hrsdc.gc.ca

  11. http://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdfhttp://www2.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

  12. Mathematics Quantitative Literacy School Numeracy Numeracy Number Sense Literacy v v

  13. SCANS COMPETENCIESTHAT REQUIRE NUMERACYSecretary’s Commission on Achieving Necessary Skills (SCANS) • Planning problems – Allocating money, time, space, staff • Systems and processes problems – understanding, monitoring, and designing social, physical, or business systems • Interpersonal problems- working in teams, negotiating, teaching, learning • Information problems – Gathering and organizing data, evaluating data, communicating about data outcomes in oral and written formats • Technology problems – developing, using, choosing, and maintaining equipment From Packer, 2001 What Mathematics Should Everyone Know and Be Able to Do?

  14. The skills of reading • The National Reading Panel Report identifies five basic skillsets required for efficient reading: • Phonemic awareness • Phonics • Fluency • Vocabulary • Comprehension (From Dr Lewis, Class 01)

  15. Adding It Up (NRC 2001 Ch. 4)Five Strands of Math Proficiency • Not completely independent of each other • All five are needed for proficient mathematics • Proficiency is not “all or nothing” • Develops over time • (develops with effort) • Conceptual understanding • Procedural fluency • Strategic competence • Adaptive reasoning • Productive disposition

  16. NMAP • Curricular content • Learning processes • Teachers and teacher education • Instructional practices • Instructional materials • Assessment • Research policies and mechanisms

  17. NMAP • Curricular content • Learning processes • Teachers and teacher education • Instructional practices • Instructional materials • Assessment • Research policies and mechanisms

  18. How many Americans are now mathematically literate /numerate? National Adult Literacy Scale (NALS) 2001 report: < 25%

  19. Quoted from JAN DE LANGE (2001) Mathematics for Literacy http://www.maa.org/QL/pgs75_89.pdf Citing a 1990, a newspaper report:

  20. Quoted from JAN DE LANGE (2001) Mathematics for Literacy http://www.maa.org/QL/pgs75_89.pdf Citing a 1990, a newspaper report: “Yesterday, …AVRO Television paid attention to analphabetism in The Netherlands. From data collected …, it appeared that no fewer than 1 out of 25 people cannot read or write, that is, cannot read or write a shopping list, cannot follow subtitles on TV, cannot read newspapers, cannot write a letter. Just imagine, 1 out of 25 people, …which means 25% of our citizens. How many citizens does The Netherlands have? 14 million? That means that in our highly developed country no less than three and a half million cannot read or write. Aren’t you speechless?”

  21. Quoted from JAN DE LANGE (2001) Mathematics for Literacy http://www.maa.org/QL/pgs75_89.pdf … “Speechless, indeed.” “… Innumeracy, or the inability to handle numbers and data correctly and to evaluate statements regarding problems and situations that invite mental processing and estimating, is a greater problem than our society generally recognizes. According to Treffers (1991), this level of innumeracy might not be the result of content taught (or not taught) but rather the result, at least in part, of the structural design of teaching practices. “Fixing” this problem, however, requires dealing with several issues: From a mathematical perspective, how do we define literacy? Does literacy relate to mathematics (and what kind of mathematics)? What kind of competencies are we looking for? Are these competencies teachable?

  22. http://cdn.crooksandliars.com/files/uploads/2009/11/Fox%27s%2BPie%2BChart_f8430.jpghttp://cdn.crooksandliars.com/files/uploads/2009/11/Fox%27s%2BPie%2BChart_f8430.jpg

  23. Numeracy and Decision MakingPeters, Vastfjall, Slovic, et al., Psychological Science, 2006

  24. Numeracy and Decision MakingPeters, Vastfjall, Slovic, et al., Psychological Science, 2006 • “Rate how well Anne did on a scale of -3 to 3” • “Anne received 24% incorrect” (neg) vs. • “Anne received 76% correct”(positive)

  25. Numeracy and Decision MakingPeters, Vastfjall, Slovic, et al., Psychological Science, 2006 • “Rate how well Anne did on a scale of -3 to 3” • “Anne received 24% incorrect” (negative frame) vs. • “Anne received 76% correct”(positive)

  26. Numeracy and Decision MakingPeters, Vastfjall, Slovic, et al., Psychological Science, 2006 “10 out of every 100 patients similar to Anne commit an act of violence” vs “10% of patients similar to Anne commit an act of violence” “Rate the risk of Anne hurting someone on a scale of 1 (low) to 6 (high)” • “Rate how well Anne did on a scale of -3 to 3” • “Anne received 24% incorrect” (neg) vs. • “Anne received 76% correct”(positive)

  27. Numeracy and Decision MakingPeters, Vastfjall, Slovic, et al., Psychological Science, 2006 “10 out of every 100 patients similar to Anne commit an act of violence” vs “10% of patients similar to Anne commit an act of violence” “Rate the risk of Anne hurting someone on a scale of 1 (low) to 6 (high)” • “Rate how well Anne did on a scale of -3 to 3” • “Anne received 24% incorrect” (neg) vs. • “Anne received 76% correct”(positive)

  28. To me, mathematics is: I use math to: How do I feel about math? I _________ it, because

  29. Do teachers’ attitudes about math affect their students’ math achievement?Beilock, Gunderson, Ramirez, and Levine PNAS 2010

  30. Do teachers’ attitudes about math affect their students’ math achievement?Beilock, Gunderson, Ramirez, and Levine PNAS 2010 • Ss: • 117 students (65 girls and 52 boys); first graders and second graders • 17 first- and second-grade teachers (12 first-grade and 5 second-grade) with an average of 13 years of teaching experience (SD = 9.20). (all female) • Student testing done twice: during fall and spring of the school year. • Woodcock–Johnson III Applied Problems subtest • Gender ability beliefs (via drawings) • Teachers completed • sMARS

  31. Do teachers’ attitudes about math affect their students’ math achievement?Beilock, Gunderson, Ramirez, and Levine PNAS 2010 • Teachers’ Math Anxiety and student achievement: • FALL semester: (no relation for boys or girls) • Teachers’ Math Anxiety and students’ traditional gender ability beliefs: • FALL semester: No relation for boys or girls

  32. Do teachers’ attitudes about math affect their students’ math achievement?Beilock, Gunderson, Ramirez, and Levine PNAS 2010 • Teachers’ Math Anxiety and student achievement: • FALL semester: (no relation for boys or girls) • END of school year: -Correlation among girls (r = −0.28, P = 0.022) • but not among boys (r = −0.04, P = 0.81) • Teachers’ Math Anxiety and students’ traditional gender ability beliefs: • FALL semester: No relation for boys or girls • END of school year: +Correlation among girls (r = 0.28, P = 0.022) • but NOT among boys, (r = 0.09, P = 0.52).

  33. Female teachers’ math anxiety affects girls’ math achievementBeilock, Gunderson, Ramirez, and Levine PNAS 2010

  34. Do teachers’ attitudes about math affect their students’ math achievement?Beilock, Gunderson, Ramirez, and Levine PNAS 2010 “…math anxiety can be reduced through math training and education. …mathematics requirements for obtaining an elementary education degree at most U.S. universities need to be rethought. … to teach … students effectively, more care needs to be taken to develop both strong math skills and positive math attitudes in …educators.” Gresham G (2007) A study of mathematics anxiety in pre-service teachers. Early Childhood Education Journal 35:181–188.

  35. Female teachers’ math anxiety affects girls’ math achievementBeilock, Gunderson, Ramirez, and Levine PNAS 2010 ?

  36. Female teachers’ math anxiety affects girls’ math achievementBeilock, Gunderson, Ramirez, and Levine PNAS 2010

  37. Ashcraft: Attitudes about math can… • affect achievement level • affect coursework selection • be influenced by stereotype threat • affect poor and successful math achievers, but poor performers are at higher risk (e.g., Ashcraft) • be influenced by teachers: High demand for accuracy low cognitive or motivational support during class leads to more math anxiety in students, esp. those vulnerable to math anxiety.

  38. A proposed framework for understanding math anxiety – from Ashcraft et al., 2007, in Why is Math So Hard for Some Children? ____________________________________________________________ Math anxiety, Anxious responding Math performance deficits and avoidance Adequate mastery and performance Cognitive biases: Negative attitudes about math Vulnerability to anxiety Adequate skill, motivation, working memory Inadequate skill, motivation, working memory Learning history, biological predisposition

  39. Gave 60 women (college students) difficult math test with 7 problems (All Ss attempted all 7 problems) Thought listing task preceded each problem. 2005

  40. Threat condition: ‘‘recent research has shown that there are clear differences in the scores obtained by men and women in logical-mathematical tasks.’’ Control: ‘‘there are no differences between men and women in logical-mathematical tasks.’’ 2005

  41. % correct in Threat condition minus % correct in Control condition Negative values indicate better performance in the CONTROL condition. Numbers 1 – 7 indicate test item

  42. % correct in Threat condition minus % correct in control condition Negative values indicate better performance in the CONTROL condition. Numbers 1 – 7 indicate test item

  43. negative math-related thoughts (e.g., ‘‘These exercises are too difficult for me”; ‘‘I am not good at math’’); • hate for math, including thoughts like ‘‘I have always hated math’’ • generic distress, (e.g., ‘‘I’m tired’’ or ‘‘It is hot’’) • self-confidence (e.g., ‘‘I’m really good at this) • neutral reference to the test, (e.g.,‘‘Probably none of these alternatives is correct’’) • not knowing what to write, like ‘‘I don’t know what to write’’ • guess, e.g.,‘‘I had no clue on this one’’ • other, (e.g., ‘‘pizza’’) 2005

  44. 2005

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