Numeracy Can Learn from Literacy 5/15/2008 The Great Reading Debate: Phonics vs. Whole Language What Numeracy Can Phonics: Whole Language: Symbol patterns Reading for meaning Learn From Literacy… Memorization Context based Reading words Motivational Back to basics Free reading Skills drills “Inventive” spelling, Spelling tests grammar, punctuation, Eric Gaze etc. Reductionist Alfred University Holistic/Constructivist History: Whole Math? 18th Century: Reading Primers and Phonics 1989 NCTM Standards: conceptual understanding and problem solving skills 19th Century: Horace Mann against phonics led to “look-say” i.e. Dick and Jane 1994 Reform Calculus: Harvard text Hughes-Hallett et.al. 1950’s: Rudolf Flesch’s Why Johnny Can’t 1997 “Reform Calculus has been a disaster”!? Read back to phonics 2000 Math tutoring franchises 1980’s: Whole Language March 13, 2008 National Math Panel: “America’s 1990’s NAEP Reading Scores Decline math education system is broken” “curriculum must simultaneously develop conceptual 2000: Back to basics understanding, computational fluency, and problem solving” Literacy: reading and writing? Acquisition vs. Learning John Fee: What is Literacy? Acquisition: subconscious by exposure to models and A discourse: “identity kit” for a socially meaningful experimentation, i.e. constructivist group i.e. woman, American, middle class, factory worker, etc. Learning: conscious by teaching, explanation and analysis of component parts, i.e. reductionist Primary discourse: family; all others secondary. Patricia Cline Cohen Emergence of Numeracy: Literacy: control of language in a commercial arithmetic texts 1800: board feet for secondary discourse houses, cost per yard of cloth, problem based memory learning Many literacies! Numeracy: control of numbers in context 1820’s: New Math! Discovery based 2008GazeNNN6up.pdf 1 Numeracy Can Learn from Literacy 5/15/2008 Acquisition AND Learning Transfer and Schemata Balanced Literacy: Cultural Literacy by E.D. Hirsch Jr. Emphasize acquisition in context, with “successful communication depends on learning for transfer shared associations” Embedded Literacy: Just in Time Learning “literacy requires us to have intensive Applications and Misapplications of Cognitive knowledge of relationships and extensive Psychology to Mathematics Education knowledge of specifics” Anderson/Reder/Simon: Critique extreme constructivism and situated learning Need to include ability to transfer as a “a well developed schema helps us specific goal in instruction manipulate and connect information rapidly” Graphs Odds Equations Mass Balance Tables Exponential Functions! Numeracy Phonics: Growth Factor Growth (relationshipsBest Fitbetween quantities) Percentages! Slope Linear Percentiles Percent MPH Growth Ratio: A comparison of the relative size Change Rate of DeathRates! Rate Change of 2 quantities. The ratio of Qty. A to Fractions Regression APR Qty. B is 2:3 means for every 2 A units Conversions Poverty Rate Mean RATIOS! we have 3 B units. Percentage Rate: A ratio between quantities (typically with Exchange Rate Decimals nd Conversions! Trend-line different units); with the 2 qty typically scaled to 1 Conversion Factor Least Squares and read with “per”, i.e. mph, mpg, etc. Scale Z-scores Percentage: A rate with 2nd quantity scaled to 100. Units Scaling Factor Standard Conversion: A ratio indicating a change in units. Deviation Scales! Standard Change in Proportions Scale: A ratio indicating a change in magnitude. Scores Magnitude Proportionality E=mc^2 Coefficient of Variation Skills Drills Age Dependency Ratios The ratio of boys to girls is 2 : 3, if there are The age dependency ratio, is derived by 10 boys how many girls? dividing the combined under-18 and 65-and- over populations by the 18-to-64 population 2/3 = 10/x…2x = 30… and multiplying by 100. 15 girls! (73.9 +37.9)/189.8 = 0.589 * 100 = 58.9 You get 18 out of 20 questions correct. What Use 58.9 in a sentence… percentage of the questions did you answer The ratio of under 18 and 65+ to 18-64 year correctly? olds is 58.9 to ….???? 18/20 = 0.9…. 58.9 : 1 ??? 58.9% of the people aged 18- 90% correct! 58.9% ??? 64 years old are actually both under 18 AND over 65 years old! 2008GazeNNN6up.pdf 2 Numeracy Can Learn from Literacy 5/15/2008 2008 Math Panel RE-Emphasis on algebra Bernard Madison Articulation and QL: GATC sequence in high school mathematics Myopic focus on Calculus preparation abandons middle school math numeracy topics! Two-thirds of Fall 2005 math enrollments are remedial/introductory math (CBMS) “Reform Calculus is Dead!” 25 PPI zoomed in 3200% 25 PPI Algebra in context…modeling, statistics, etc. Absences and Grades, Math 7, 2006-2007 Insanity (n): 100 y = -0.8875x + 88.292 90 R2 = 0.2096 80 Keep doing the same thing over and over and 70 expect different results. -MMB 60 50 40 Final Average 30 20 ˆ (X X ) 10 Y Y rxy SDy 0 SD 0 5 10 15 20x 25 30 35 40 45 or Number of Absences SD SD ˆ y y Y rxy X Y rxy X SDx SDx 2008GazeNNN6up.pdf 3.