Assessing Mathematics by Steven Leinwand

1. Assessing Mathematicsby Steven Leinwand Jim Greene March 19, 2012

2. The 10 Instructional Shifts • Incorporate ongoing cumulative review into every day’s lesson • Adapt what we know works in our reading programs and apply it to mathematics instruction • Use multiple representations of mathematical entities • Create language-rich classroom routines • Take every available opportunity to support the development of number sense Distrubted Leadership – Assessible Mathematics

3. Continued • Build from graphs, charts, and tables • Tie the math to such questions as: “How big?” How much?” “How far?” to increase the natural use of measurement throughout the curriculum • Minimize what is no longer important • Embed the mathematics in realistic problems and real-world contexts • Make “Why?” “How do you know?” “Can you explain?” classroom mantras Distrubted Leadership – Assessible Mathematics

4. Different ApproachesU.S. vs. Japan • In the U.S. and Germany – focus is on skill acquisition. U.S.A ranks 23 in Mathematical proficiency of 15 yr. olds • In a typical class … • Teacher instructs student in a concept or skill • Teacher solves example problems with the students • Students practice on their own while teacher helps individual students Distrubted Leadership – Assessible Mathematics

5. in Japan … • In Japan, focus is on understanding. Japan ranks 3 in mathematical proficiency of 15 year olds. • In a typical class: • Teacher poses a complex, thought-provoking problem • Students struggle with the problem • Various students present ideas or solutions to the problem • Class discusses various solution methods • Teacher summarizes the class conclusions • Students practice similar problems Distrubted Leadership – Assessible Mathematics

6. Ready, Set, Review Distrubted Leadership – Assessible Mathematics

7. Incorporate ongoing cumulative review into every day’s lesson Mini-Math Review • 6 x 7 = • What number is 1000 less than 18,294? • About how much is $0.29 and $0.32? • What is 1/10 of 450? • Draw a picture of 1_2/3 • Estimate my weight in kilograms Distrubted Leadership – Assessible Mathematics

8. Adapt what we know works in our reading programs and apply it to mathematics instruction Distrubted Leadership – Assessible Mathematics

9. “Jane went to the store.” Can you read that sentence aloud? • Can you tell me where Jane went? • Can you tell me who went to the store? • Can you tell me why Jane might have gone to the store? • Did it make sense for Jane to go to the store? Distrubted Leadership – Assessible Mathematics

10. Use multiple representations of mathematical entities Distrubted Leadership – Assessible Mathematics

11. Picture it, draw it Find a model to visualize it Distrubted Leadership – Assessible Mathematics

12. Create language-rich classroom routines • Two odd numbers • Two digit number • Two numbers 10 apart Distrubted Leadership – Assessible Mathematics

13. MARCH MADNESS BONUS Question – In a rough and tumble basketball game where you can score one point for a foul shot, two points for a basket, and three points on long, 3 point shots. The score was 63 to 63 with three minutes to go. The Owls went on a 10–0 run and beat the Vultures 73 – 63. How many different ways could the owls have scored the 10 unanswered points? Distrubted Leadership – Assessible Mathematics

14. Take every available opportunity to support the development of number sense • Example of … • Mixed number • Whole number • Fraction Distrubted Leadership – Assessible Mathematics

15. Build from graphs, charts, and tables Milking the data… Distrubted Leadership – Assessible Mathematics

16. Tie the math to such questions as: “How big?” How much? How far? To increase the natural use of measurement throughout the curriculum • Ex. If someone is 50 years old, how old is that person if time age is measured in days? • Try this one … how old are you in days? Distrubted Leadership – Assessible Mathematics

17. Minimize what is no longer important • Time to throw out the bath water … • When was the last time you multiplied 2953 by 15.9 (by hand)? • Or added 1/7 + 2/9 in a real life problem? Distrubted Leadership – Assessible Mathematics

18. Embed the mathematics in realistic problems and real-world contexts • If you knew that Peter Dowdeswell of London, England, holds the world record for pancake consumption . . . • What questions might your students have about this record? Distrubted Leadership – Assessible Mathematics

19. Father Judge Wing Bowl Revisited … • He consumed 62 pancakes each 6 inches in diameter and 3/8 inches thick, with butter and syrup, in 6 minutes and 58.5 seconds. • How big a stack is that? • At what rate did he eat the pancakes? • Could you graph his progress? Distrubted Leadership – Assessible Mathematics

20. Can You Label The Chart? Distrubted Leadership – Assessible Mathematics

21. Make “why?” “How do you know?” Can you explain? Classroom mantras Distrubted Leadership – Assessible Mathematics

22. Another Resource … Distrubted Leadership – Assessible Mathematics

23. Your Thoughts or Comments … Distrubted Leadership – Assessible Mathematics