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# Mtf example

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### Mtf example

1. 1. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematical Task Framework in Action Recognizing Why We Rarely Get the Level of Student Understanding We Want Friday, November 19, 2010
2. 2. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Why do students struggle with challenging concepts and problems? • Studies suggest low engagement in mathematics instruction and practice • What if we use quality instructional materials? • Still poor higher order thinking skills suggests other issues in students’ instruction • Let’s check out an example Friday, November 19, 2010
3. 3. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit An Example in Practice Find a pattern for the sum of the interior angles of a polygon. xº xº xº Friday, November 19, 2010
4. 4. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Method 1: Find a pattern for the sum of the interior angles of a polygon. • Teachers pose the problem and ask students to measure angles in various triangles, quadrilaterals, and polygons. • Students are asked to identify possible patterns in their data for different polygons. • Students predict the sum of interior angles for polygons that they did not measure or diagram. • Students try to generate a rule for the sum of all angles based on the number of sides. Friday, November 19, 2010
5. 5. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit An Example in Practice Find a pattern for the sum of the interior angles of a polygon. xº xº yº zº xº zº wº yº yº zº wº vº x + y + z ≈ 180˚ w + x + y + z ≈ 360˚ v + w + x + y + z ≈ 540˚ Friday, November 19, 2010
6. 6. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Method 2: Find a pattern for the sum of the interior angles of a polygon. • Teachers pose the problem and ask students to measure angles in various triangles, quadrilaterals, and polygons. • Students are shown that any polygon can be “broken down” into triangles by drawing diagonals from one “corner” of the object, making two less triangles than sides. • Students are told that there are 180º in a triangle, and so the sum is 180 x (the number of sides - 2) Friday, November 19, 2010
7. 7. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit An Example in Practice Find a pattern for the sum of the interior angles of a polygon. xº Friday, November 19, 2010
8. 8. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit An Example in Practice Find a pattern for the sum of the interior angles of a polygon. xº Friday, November 19, 2010
9. 9. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills Friday, November 19, 2010
10. 10. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy Friday, November 19, 2010
11. 11. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand Friday, November 19, 2010
12. 12. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Friday, November 19, 2010
13. 13. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Friday, November 19, 2010
14. 14. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Friday, November 19, 2010
15. 15. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Friday, November 19, 2010
16. 16. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Friday, November 19, 2010
17. 17. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Friday, November 19, 2010
18. 18. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Friday, November 19, 2010
19. 19. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Friday, November 19, 2010
20. 20. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Analysis Friday, November 19, 2010
21. 21. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Analysis Friday, November 19, 2010
22. 22. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Analysis Synthesis Friday, November 19, 2010
23. 23. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Analysis Synthesis Friday, November 19, 2010
24. 24. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Higher Order Thinking Skills • Bloom’s Taxonomy • Tasks vary in their cognitive demand • More complicated tasks need to be practiced and internalized. Knowledge Comprehension Application Analysis Synthesis Evaluation Friday, November 19, 2010
25. 25. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework from Stein and Smith, 1998 Friday, November 19, 2010
26. 26. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials from Stein and Smith, 1998 Friday, November 19, 2010
27. 27. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials from Stein and Smith, 1998 Friday, November 19, 2010
28. 28. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials Tasks as set up by teachers from Stein and Smith, 1998 Friday, November 19, 2010
29. 29. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials Tasks as set up by teachers from Stein and Smith, 1998 Friday, November 19, 2010
30. 30. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students from Stein and Smith, 1998 Friday, November 19, 2010
31. 31. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students from Stein and Smith, 1998 Friday, November 19, 2010
32. 32. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit The Mathematics Task Framework Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students Student learning from Stein and Smith, 1998 Friday, November 19, 2010
33. 33. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit MTF in Action Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students Student learning Method 2 Method 1 Friday, November 19, 2010
34. 34. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit MTF in Action Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students Student learning Curriculum Teachers Enactment Understanding Method 2 Method 1 Friday, November 19, 2010
35. 35. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit MTF in Action Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students Student learning Curriculum Teachers Enactment Understanding Method 2 Method 1 Friday, November 19, 2010
36. 36. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit MTF in Action Tasks as they appear in curriculum materials Tasks as set up by teachers Tasks as enacted by teachers and students Student learning Curriculum Teachers Enactment Understanding Method 2 Method 1 Friday, November 19, 2010
37. 37. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Insights from cognitive biology... • Brain activity and the ability to effectively apply prior knowledge is related to the complexity of a task. • Tasks that are too difﬁcult and beyond the scope of conceptualizing cause the cognitive centers to “shut down” • Similarly, simple tasks, such as memorization, simple application, and the use of algorithms to “solve” a problem, generally cause the brain to disengage (i.e. boredom) • Endorphins are released when the brain is engaged over time in relatively complex tasks (“the pleasure of ﬁnding things out”) Friday, November 19, 2010
38. 38. middlestart The National Forum for Middle Grades Reform Mathematics Improvement Toolkit Insights from educational research • Signiﬁcant research addresses the need to support “high-level” thinking and problem solving in schools, showing clear beneﬁts to learning mathematics • TIMSS Video Study explored international variation - In high achieving countries, when problems addressing both skill and conceptual knowledge were posed, students studied the relationships and connections often (about 50%) - In the U.S., students never got the chance - over 99% of teachers stepped in to do the conceptual work, leaving only skill development. - U.S. students spend all of their time focusing on skills. Friday, November 19, 2010