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Kansas City 2/10/2012

Kansas City 2/10/2012. Cathy Battles Kansas City Regional Professional Development Center battlesc@umkc.edu. DO NOW/WARM-UP. Start with the number of feet in a yard Multiply by the number of sides of a quadrilateral Divide by the number of inches in a foot

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Kansas City 2/10/2012

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  1. Kansas City2/10/2012 Cathy Battles Kansas City Regional Professional Development Center battlesc@umkc.edu

  2. DO NOW/WARM-UP • Start with the number of feet in a yard • Multiply by the number of sides of a quadrilateral • Divide by the number of inches in a foot • Multiply by the number of cm in a meter • Divide by the number of years in a decade • Add the number of angles in a pentagon

  3. Answer 15

  4. The Show-Me Standards – PERFORMANCE (to do) GOAL 1 GOAL 3 recognize and solve problems gather, analyze and apply information and ideas 1.6, 1.10 3.2, 3.5 GOAL 2 GOAL 4 make decisions and act as responsible members of society communicate effectively within and beyond the classroom 2.2

  5. N1b Big Idea Content/ Performance Standards GLE Strand DOK Concept GLEs/CLEs Number and Operations

  6. DEPTH OF KNOWLEDGE • Level 1 Recall Recall of a fact, information, or procedure. • Level 2 Skill/Concept Use information or conceptual knowledge, two or more steps, etc.; you do something • Level 3 Strategic Thinking Requires reasoning, developing plan or a sequence of steps, some complexity, more than one possible answer; generates discussion • Level 4 Extended Thinking Requires an investigation, time to think and process multiple conditions of the problem

  7. Complexity vs. Difficulty An item may be difficult but have no relationship to higher levels of DOK.

  8. DOK is not about difficulty Difficulty is a reference to how many students answer a question correctly. How many of you know the definition of exaggerate? DOK 1 – recall If all of your students know the definition, this question is an easy question. How many of you know the definition of prescient? DOK 1 – recall If most of your students do not know the definition, this question is difficult. 8

  9. DOK is about what follows the verb What comes after the verb is more important than the verb itself. “Analyze this sentence to decide if the commas have been used correctly” does not meet the criteria for high cognitive processing. The student who has been taught the rule for using commas is merely using the rule. 9

  10. DOK and the GLEs & the CLEs • The assigned DOK to the GLEs & CLEs is the ceiling for the MAP test only. • Our classroom instruction will most likely go above and beyond what is coded to each GLE or CLE

  11. The class went on a field trip. The students left school at 9:00 a.m. They returned to class at 1:30 p.m. How long were they gone?A 8 hr 30 minB 8 hrC 4 hr 30 minD 4 hr Level 2. The choices offered indicate that this item is intended to identify students who would simply subtract 9 minus 1 to get an 8. More than one step is required here. The students must first recognize the difference between a.m. and p.m. and make some decisions about how to make this into a subtraction problem, then do the subtraction. Grade 4

  12. Think carefully about the following question. Write a complete answer. You may use drawings, words, and numbers to explain your answer. Be sure to show all of your work. Laura wanted to enter the number 8375 into her calculator. By mistake, she entered the number 8275. Without clearing the calculator, how could she correct her mistake? Explain your reasoning. Level 3 An activity that has more than one possible answer and requires students to justify the response they give would most likely be a Level 3. Since there are multiple possible approaches to this problem, the student must make strategic decisions about how to proceed, which is more cognitively complex than simply applying a set procedure or skill.

  13. Mathematics The school newspaper conducted a survey about which ingredient was most preferred as a pizza topping. This graph appeared in the newspaper article. Level 2 What information would best help you determine the number of people surveyed who preferred sausage? A number of people surveyed and type of survey used B type of survey used and ages of people surveyed C percent values shown on chart and number of people surveyed D ages of people surveyed and percent values shown on chart

  14. Math Content Blueprints

  15. Supporting Mathematics Learning • Research indicates that if effective Tier 1 instruction is in place, approximately 80% of students’ with mathematical learning difficulties can be prevented. (Gersten et al. 2009a; Wixon 2011) Administrator’s Guide: Interpreting the Common Core State Standards to Improve Mathematics Education (NCTM, 2010)

  16. EQUIVALENCY TRUE OR NOT TRUE?

  17. EQUIVALENCY TRUE OR NOT TRUE?

  18. EQUIVALENCY TRUE OR NOT TRUE?

  19. EQUIVALENCY TRUE OR NOT TRUE?

  20. The first example is called stringing/run-on which will not be accepted as a correct process. The second example is an acceptable process. Because direction changes 24 X 4 is not interpreted as being equal to 201.

  21. When researchers asked first- through sixth-grade students what number should be placed on the line to make the number sentence 8 + 4 =  + 5 true, they found that fewer than 10 percent in any grade gave the correct answer—that performance did not improve with age.  How the Brain Learns Mathematics David Sousa 2008

  22. Number Sentence • mathematical statement(equation) in which equal values appear to the right and left of an equal sign or comparisons written horizontally. • Examples: 3 + 4 = 7, 8 – 2 = 6, 3 + 4 = 2 + 5, 7 > 6.

  23. Equations • If the problem asks for an equation, but the student gives an expression, the answer is considered to be incorrect. • If the problem asks for an expression, but the student gives an equation, the answer is considered to be incorrect.

  24. Equations cont. • Write an equation for profit of x items if it costs $2.75 to manufacture each item and the item sells $3.20 • A correct equation: P =$3.20x-$2.75x • Incorrect equation: Profit=$3.20x-$2.75x

  25. Patterns You must have at least 3 numbers to determine a pattern. 1, 4, . . . is not enough to determine a pattern. There could be many possible answers. (1, 4, 16, 64, . . . or 1, 4, 7, 10, . . .)

  26. Rules for Patterns When students are asked to find a rule (for a pattern), they should providea general statement, written in numbers and variables or words, that describes how to determine any term in the pattern. Example: 5, 8, 11, 14, . . . The first term is 5. Add 3 to each term to get the next term. Rules (or generalizations) for patterns can be written in either recursive or explicit notation.

  27. Describing or Explaining a pattern… should include the beginning term and the procedure for finding any subsequent term. Describing or explaining how to find the next term in a pattern… Example: add 5 Example: multiply by 7 Example: multiply 6 times 3 and add 1

  28. Explicit Notation In the explicit form of pattern generalization, the formula or rule is related to the order of the terms in the sequence and focuses on the relationship between the independent variable (x) or the number representing the term number (n) in the sequence and the dependent variable (y) or the term (t) in the sequence. Example: 5n Example: 3n – 1 Example: 4x + 7 2n - 2

  29. Recursive Notation Middle School Example: 7, 10, 13… First Now = 7, Next = Now + 3 OR In the recursive form of pattern generalization, the rule focuses on the change from one element to the next. High School Example: 5, 9, 13… a1 = 5 , an= an= nth term a1 = first term an – 1 = previous term an-1 + 4

  30. ARRAY • A set of objects in equal rows and equal columns. When describing, the number of rows should come first followed by the number of columns. Arrays are used in describing a multiplication problem. A pictorial representation of 3 X 2 means there are 3 rows with 2 objects in each row. If a student were to draw 2 rows with 3 objects in each row, it would not be correct.

  31. Discrete vs. Continuous Data Discrete data is data that can be counted. (You can’t have a half a person). Continuous data can be assigned an infinite number of values between whole numbers. (Time, length, etc.)

  32. Terminology/Vocabulary • Use appropriate mathematical terminology • rhombus not diamond • Watch for multiple meaning words • table, plane, even, odd, degree, mean, median, prime • Homophones • sum and some • two and too

  33. Use Sentence Frames for Students with Language Difficulties or Language Impairments

  34. Graphs If no scales are included on a graph: Students can assign any scale they wish It is assumed the scale is 1 A broken axis, with other intervals consistent, means the intervals between zero and the first increment are compressed one are compressed

  35. Meta-analysis researchBest practice families of strategies 1. Finding similarities & differences 45% 2. Summarizing & note taking 34% 3. Reinforcing effort & providing recognition 29% 4. Homework & practice 28% 5. Non-linguistic representations 27% 6. Cooperative learning 27% 7. Setting objectives and providing feedback 23% 8. Generating & testing hypotheses 23% 9. Cues, Questions & advance organizers 22% Classroom Instruction That Works: Based on meta-analysis by Marzano, Pickering & Pollock

  36. Conceptually Engaging Tasks = Cognitively Demanding Tasks Silver, E. (2010). Examining what teacher do when they display best practice: Teaching mathematics for understanding. Journal of Mathematics Education at Teachers’ College. 1(1), 1-6. High cognitive demand lessons provide opportunities for students: • To explain, describe, justify, compare, or assess; • To make decisions and choices • To plan and formulate questions • To exhibit creativity; and • To work with more than one representation in a meaningful way.

  37. What Makes a Difference Darling-Hammond, L. (2006) 2006 DeWitt Wallace-Reader’s Digest Distinguished Lecture – Securing the right to learn. Policy and practice for powerful teaching and learning. Educational Researcher, 35(7), 13 – 24. The quality of teachers and teaching. Access to challenging curriculum, which ultimately determines a greater quotient of students’ achievement than their initial ability levels; and Schools and classes organized so that students are well known and well supported.

  38. Effective Instruction Hiebert, J., & Grouws, D. A. (2006). Research analysis: Which instructional methods are most effective? Reston, VA: National Council of Teachers of Mathematics. Research on effective teaching has not suggested a direct association between a single method of teaching and a resulting goal…Research points to…certain features of instruction that result in improved student learning.

  39. Some Features of Mathematical Practice of Effective Instruction – T2 TASKS Conceptual Engagement & Productive Struggle TALK Mathematical Discourse

  40. 3rd Grade Released 2006

  41. 4th Grade Released 2006

  42. 5th Grade Released 2006

  43. 6th Grade Released 2006

  44. 7th Grade Released 2006

  45. 8th Grade Released 2006

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