2. Leading the Way to Accelerating Math Achievement Bill Hanlon

3. What are you doing to improve instruction?

4. ~ 5 Essentials ~ Organizing Student Learning Instruction Note taking Homework Test Preparation Assessment

5. Organizing Student Learning

6. Answering the Question: What are you doing to help my child learn?

7. Rules in Mathematics Don’t make sense!

8. Good News! Teachers are already employing many of the best practices needed to increase student achievement.

9. Best practices Note taking Homework Tests

10. Components of an Effective Lesson Before presenting a lesson, refer to the assessment blueprint for the unit. Introduction Daily Reviews Daily Objective Concept and Skill Development and Application Guided / Independent / Group Practice Homework Assignments Closure Long-Term Memory Review

11. Build on Strengths

12. What’s needed? Refinement & Reinforcement of those practices.

13. Quiet Conversions Change is difficult for people. Culture: If I wait long enough, this too will pass

14. Best Practices Relentlessly supporting best practices will eventually crowd out poor instructional strategies.

15. Leadership Lead by demonstrating success in classrooms where teachers will modify their instruction to increase student achievement.

16. Build Trust & Confidence Students will work for teachers for no other reason than loyalty. Law of Reciprocity

17. Increasing Student Achievement No simple answer- what works is work

18. It’s about you!!! You cannot and should not depend on products, programs or services to address the needs of your student population, close the achievement gap or increase student achievement.

19. Actions follow beliefs 10 simple 2-letter words

20. If it is to be, it is up to me

21. 2 Standards My Kid Common Sense

22. My Kid Standard Treat the kids in your school or classroom the same way you want your own kids treated.

23. Common Sense Standard Appeal to teachers common sense and experience, do not get into a citation battle.

24. Learning Students learn best when they are given feedback on their performance and praised for doing things well

25. Student-Teacher Relationships 1. Treat your students the way you want your own children treated. 2. Build success on success. 3. Talk to your students. Be friendly. 4. Talk positively to your students about their opportunity to be successful. 5. Call home early with information and good news. 6. Make testing as much a reflection of your instruction as their studying. 7. Teach your students how to study effectively and efficiently (visual, audio, kinesthetic, concentration time). 8. Tell them you like them. 9. Go over expectations explicitly and give examples. 10. Build trust, make sure they know you are there for them by telling them you are. 11. Tell them you want them to succeed. 12. Continually answer the question; “What am I doing to help my students learn?”

26. Success on Success –Teach students how to learn effectively and efficiently. auditory visual kinesthetic Concentration times

27. Studying Reading Thinking Reflecting Organizing Writing Analyzing Visualizing Reviewing Remembering Recalling

28. Study skills Good students adjust studying according to several factors: –the demand of the material –the time available for studying –what they already know about the topic –the purpose & importance of assignment –the standards they must meet

29. Study skills Good students space learning sessions over time and do not cram Good students identify the main idea in new information, connect new material to what they already know, and draw inferences about its significance Good students make sure their study methods are working properly by frequently appraising their own progress

30. Expectation - Goals Being the best! What does it take to be the best? What are you willing to do?

31. Math Wars It’s not traditionalist vs. constructivist, students need to get the whole picture.

32. Balance Vocabulary & Notation Concept Development & Linkage Memorization of Important Facts & Procedure Applications Appropriate Use of Technology Balance in mathematics has been defined as: Balance should be reflected in assessments and in the delivery of instruction.

33. Vocabulary & Notation There is no more single important factor that effects student achievement than vocabulary and notation

34. Vocabulary Find the degree of 4x 2 y 3 x 5

35. Vocabulary Best Bet? –Bet A Probability of winning is 3/5 –Bet B Odds of winning 3 to 5

36. Language Acquisition Double meanings area volume operation power mean feet product

37. 1st Essential - Instruction

38. Time on Task Stake and local school districts usually determine the classroom time available to teachers and students. However, regardless of the quantity of time allocated to classroom instruction, it is the classroom teacher and school administrator who determine the effectiveness of the time allotted. According to a survey conducted by the American Association of School Administrators, teachers identify student discipline as the single greatest factor that decreases time on task in the classroom. Generally, teachers with well-managed classrooms, have fewer disciplinary problems. These classrooms typically have teachers who have established rules and procedures are in the classroom when the students arrive, and begin class promptly. They reduce the “wear and tear” on themselves and students by establishing procedures for make-up work, they arrange their room to accommodate their teaching philosophy and style, and they develop routines that increase overall efficiency. The benefits of establishing these classroom procedures and routines become apparent as the total time on task approaches the allocated time. When teachers begin class immediately, students view them as better prepared, more organized and systematic in instruction, and better able to explain the material. Students also see these teachers as better classroom managers, friendlier, less punitive, more consistent and predictable, and as one who values student learning. Routines like beginning class immediately, reviewing recently taught material, orally reciting new material, having students take notes, and ending the class by reviewing important definitions, formulas, algorithms, and the daily objective keep students engaged and on task. Quality time on task is not a “silver bullet” that can cure all the problems facing education. However, it can play an important role in increasing student achievement.

39. Content - Instruction What you teach affects student achievement How you teach it affects student achievement

40. Subtraction 5 – 115 – 68 – 814 – 6 13 – 59 – 215 – 97 – 1 14 – 516 – 94 – 410 – 4 6 –212 – 410 – 36 – 3

41. When will I ever use this? Pythagorean Theorem Parabola Circumference

42. Knowledge, Interest, & Enthusiasm

43. Use simple straight forward examples that clarify what you are teaching. Do not get bogged down in arithmetic.

44. Multiplication by 11 by 25

45. Leading the department Leaders make sure all department members know what and how material is assessed and what a good answer looks like. Leaders make sure all members teach and assess the standards on high-stakes tests.

46. Different Ways to Measure the Same Standard

47. Finding Measures of Central Tendency 1.Find the mean of the following data: 78, 74, 81, 83, and 82. 2.In Ted’s class of thirty students, the average on the math exam was 80. Andrew’s class of twenty students had an average 90. What was the mean of the two classes combined? 3.Ted’s bowling scores last week were 85, 89, and 101. What score would he have to make on his next game to have a mean of 105?

48. Finding Measures of Central Tendency 4.One of your students was absent on the day of the test. The class average for the 24 students present was 75%. After the other student took the test, the mean increased to 76%. What was the last student’s score on the test? 5.Use the graph to find the mean.

49. I can’t teach __________ because my kids don’t know _____________

50. Show them how - Linkage Introduce new concepts using familiar language Review and reinforce Compare and contrast Teach in a different context

51. Add / Subtract Rational Expressions

52. 1 + 3 1 2 2 6 5 6 3 6 +

53. 1 + 3 1 2 = 5 6 1 + 4 1 5 = 9 20 1 + 3 1 4 = 7 12

54. 1 + 3 1 5 = 8 15

55. 2 + 3 1 5 = 13 15 3 + 10 2 3 = 29 30

56. 3 + 4 1 5 = 20 + 4 1 3 5 = 19

57. A + B C D = AD + BC BD A C + B D =

58. 2 + X 3 Y = XY 2 + X 3 Y = 2Y + 3X XY

59. 3 + x-1 2 x+3 = (x-1)(x+3) 3 + x-1 2 x+3 = (x-1)(x+3) 3(x+3) + 2(x-1)

60. + Polynomials

61. 6 7 2=6(100) + 7(10) + 2(1) 6 10 + 7 10 + 2 2 6 n + 7 n + 2 2 6x + 7x + 2 2

62. 5 3 2+3 4 1 = 8 7 3 (5 +3)(100) +(2 + 1)(1) = + (3 + 4)(10) (8)(100) + (3)(1) = + (7)(10) (800) + (3) =+ (70)

63. 213 = 9 8 7 (4 +3+2)(100) + (2+2+3)(1) =+ (1+6+1)(10) (9)(100) (900) + 362 412+ (7)(1) =+(8)(10) + (80) + (7) =+ 123+271 = 8 9 6 (1 +5+2)(100) + (3+2+1)(1) =+ (2+0+7)(10) (8)(100) (800) 502 + (6)(1) =+(9)(10) + (90) + (6) =+ Addition - Left to Right

64. (5x + 3x + 2) + (3x + 4x + 1) 22 = 8x + 7x + 3 2 5 3 2+3 4 1 =8 7 3 (5x + 3x ) + (3x + 4x) + (2 + 1) 22

65. Relations & Functions

66. Functions Special relation in which no 2 ordered pairs have the same 1st element.

67. Menu Hamburger ……….4 Hotdog ……………3 Sandwich …………5 00

68. 4 (H,)(Hd, )(S, )3 00 5 H, Hd, S,4 00 3 5 4 H, Hd,( S), 3 00 5

69. .50 1, 2, 3, 1 00 1 50.50 (1, ) (2, ) (3, ) (10, ? ) 1 00 1 50 Cold Drinks

70. .50 1, 2, 3, 1 00 1 50.50 (1, ) (2, ) (3, ) (10, ? ) 1 00 1 50 C = n x.50 =.50n or y = x 1212

71. 50 (1,) (4, )2 00 1 (2, )1 50 (3, ) 1 75 (4, )

72. Basic Facts & Procedures Stopping to remember basic facts interrupts the flow of thought, which negatively impacts learning.

73. Memorization Memorizing can help students absorb and retain information on which understanding and critical thought are based. The more sophisticated mental operations of analysis, synthesis, and evaluation are impossible without rapid and accurate recall of bodies of specific knowledge.

74. It is my job to teach: Reading Writing

75. Reading Assign reading Explicitly introduce vocabulary & notation Preview reading Connect reading Check understanding of reading Correct their understanding Use paper & pencil

76. Writing Definitions Procedures Linkages Applications Compare & contrast Describe what they understand Describe difficulty experienced Summarize Explain

77. Problem Solving Go back to definition Look for a pattern Make a table or list Draw a picture Guess & Check Examine a simpler case Examine a related problem Identify a sub-goal Write an equation Work backward

78. 2nd Essential - Note taking

79. Researchers - #1 Memory Aid - Writing it Down Complete homework assignment Prepare for unit test Prepare for high-stakes tests Note Taking

80. Rules and examples

81. Title Date Objective Vocabulary & Notation Pattern Development Rule Examples Variation

83. Questioning Student achievement rises when teachers ask questions that require students to apply, analyze, synthesize, and evaluate information in addition to simply recalling facts.

84. Kinds of Questions Directed Echo Cue Conceptual

85. Oral Recitation Language Acquisition Teaches students how to learn Embeds in short tem memory

86. Classroom Oral Recitation Procedure – Adding/Subtracting Fractions 1.Find a common denominator 2.Make equivalent fractions 3.Add/Subtract numerators 4.Bring down denominator 5.Reduce

87. Classroom Oral Recitation Quadratic Formula

88. Practice Guided Group Independent

89. 3rd Essential - Homework

90. Homework Homework should reflect what you say you value. –Vocabulary & Notation –Conceptual understanding & Linkage –Basic Facts & Procedures

91. Homework Page 270, 1–32 odd

92. Homework Read Sec. 9.4 - Expressions involving logarithms Define logarithm Write a procedure for converting logarithms to exponentials Explain why when multiplying log with the same base, you add the logs log (AB) = logA + logB Page 270 1 – 33 multiples of 3

93. Homework Read Sec 9.4 - Adding Fractions Define Fraction Draw a model for adding fractions Write a procedure for adding fractions Explain the link between adding fractions and decimals Page 270, 1 –33 multiples of 3

94. Reviews Recently taught material Long term review

95. Student Assessment

96. What do your students know? How do you know they know it? Assessing Student Work

97. 1 + 4 1 3 = 7 12

98. 5 + 24 7 18 = 24 = 3 4 CD = 72 18 x 4 24 x 3 = 72 Reducing Method 18/24 = 3/4

99. 18 24 = 3 4 5 = 15 72 7 = 18 28 72 + 43 72

100. 4th Essential- Test Preparation Test what you say you value: Instruction – Assessment – Balance Cumulative Questions Practice Tests - Parallel construction Setting a Date

101. Memory Aids Help your students remember

102. 5th Essential - Tests Form A ~ Form B

103. Organizing Student Learning Making the connection - Instruction to Note taking to Homework to Test Preparation to Tests

104. Organizing Student Learning Helps students focus and study more effectively and efficiently resulting in increased student achievement

105. Next steps Next steps What are you willing to do to increase student achievement? –Address linkage/concept development –Address student notes –Address homework assignments –Address test preparation –Look at yourself

106. Why Teacher Expectancies??? Concept Development Not a matter of if they are going to forget, it is a matter of when Understanding and ability to reconstruct information Test preparation; different was of measuring the “mean” Triangle Sum Theorem / Pythagorean Theorem Linkage Provides an opportunity to make students more comfortable, review & reinforce Slope, distance formula to Pythagorean Theorem, Equation of a Circle Reviews 1 st - short term knowledge, recently taught material 2 nd – long term knowledge, address mastery, student deficiencies, high stakes tests – not necessarily part of that year’s curriculum, but based on student knowledge

107. Why Teacher Expectancies??? Homework Homework should reflect what is valued, vocabulary and notation, important facts, procedures, open-ended questions on concept development Guided practice Reading – introduce vocabulary words, preview reading, relate to previous knowledge, retell the reading, summarize reading assignment Testing Make testing a reflection of your teaching Test what you value as in homework Ask questions with the same formality they are asked on high-stakes tests – avoid the disconnect

108. Why Teacher Expectancies??? Note Taking Number one memory aide – writing it down Helps students complete their homework Foundation for test preparation Teachers should be very prescriptive and directive Oral Recitation Imbeds information in short term memory Improving Student Grades Use simple, straight-forward examples that do not bog students down in arithmetic – focus on concepts being taught Teach the big idea Use practice tests

109. Improving Students’ Achievement State the day’s objective, teach it, and then tell them what you taught the and what they should have learned when you close the lesson – closure. Develop concepts. Teach to the big ideas. Link concepts to previously learned material and and/or real-world experiences. Have a positive attitude – build success on success. Treat students the same way you want your own children treated. Try these strategies: Use, simple, straightforward examples that clarify what is being taught. Use numbers in examples that allow students to focus on the concept and don’t bog students down in arithmetic.

110. Improving Students’ Achievement Incorporate guided practice to monitor student learning before assigning homework. Use practice tests to prepare students for unit tests. In first yea algebra, use multiple test versions. Tell students how you personally remembered (learned) important information. Try these strategies (continued): Use choral recitation to imbed information in short-term memory. Require students to take notes and keep notebooks. Require student reading as part of the daily assignment Require students to write about what they have learned. Use the second review period to reinforce long-term knowledge and address student deficiencies.

111. Questions for the department What does the data look like? What are the root causes and contributing factors of the data results? Do all department members know what and how material is assessed and what a good answer looks like? Do all members teach and assess the standards on high-stakes tests?

112. Questions How does the department monitor individual student progress on standards? How does staff intervene with students not meeting proficiency? What are the department’s most commonly used interventions for students not achieving? How successful are those interventions?

113. Plan –Specific –Measurable –Achievable –Relevant –Timely