2. Mansfield

3. Leading the Way to Accelerating Math Achievement Bill Hanlon

4. What are you doing to improve instruction?

5. Organizing Student Learning 5 + 1 Instruction, concept development-linkage Note taking Homework Test Preparation Assessment Bill Hanlon bill@hanlonmath.combill@hanlonmath.com 800.218.5482

6. +1 Student-teacher relationships

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

8. Rules in Mathematics Don’t make sense!

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

10. Best practices Note taking Homework Tests

11. 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

12. Build on Strengths

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

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

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

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

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

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

19. 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.

20. Actions follow beliefs 10 simple 2-letter words

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

22. 2 Standards My Kid Common Sense

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

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

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

26. 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?”

27. Unsuccessful Students

28. Contributing Factors

29. How do you see your students?

30. Contributing Factors How do your students see you?

31. Contributing Factors What are you currently doing to motivate, to address, unsuccessful students? Anything special for ELL, special education, or students living in poverty?

32. Contributing Factors Belief Systems –Teachers believing in students –Students believing in themselves –Teachers believing in themselves

33. Contributing factors What factors do you control?

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

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

36. 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

37. 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

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

39. Expectations Grade Distributions

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

41. 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.

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

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

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

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

46. MLL Math Language Acquisition

47. Speaking Oral recitation Speaking Working in pairs (groups)

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

49. 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

50. Classroom Oral Recitation Quadratic Formula

51. 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.

52. 1st Essential - Instruction

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

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

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

56. Knowledge, Interest, & Enthusiasm

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

58. Multiplication by 11 by 25

59. 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.

60. Different Ways to Measure the Same Standard

61. 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?

62. 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.

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

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

65. + Polynomials

66. 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

67. 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)

68. 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

69. (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

70. Add / Subtract Rational Expressions

71. 1 + 3 1 2 2 6 5 6 3 6 +

72. 1 + 3 1 2 = 5 6 1 + 4 1 5 = 9 20 1 + 3 1 4 = 7 12

73. 1 + 3 1 5 = 8 15

74. 2 + 3 1 5 = 13 15 3 + 10 2 3 = 29 30

75. 3 + 4 1 5 = 20 + 4 1 3 5 = 19

76. 2 + X 3 Y = XY 2 + X 3 Y = 2Y + 3X XY

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

78. 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)

79. Relations & Functions

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

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

82. 4 (H,)(Hd, )(S, )3 00 5 H, Hd, S,4 00 3 5 4 H, Hd,( S), 3 00 5

83. .50 1, 2, 3, 1 00 1 50.50 (1, ) (2, ) (3, ) (10, ? ) 1 00 1 50 Cold Drinks

84. .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

85. 50 (1,) (4, )2 00 1 (2, )1 50 (3, ) 1 75 (4, )

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

87. 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.

88. It is my job to teach: Reading Writing

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

90. Organizing Student Thinking What’s the easiest way to help students to organize their thinking? Writing

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

92. 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

93. 2nd Essential - Note taking

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

95. Rules and examples

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

98. Algebra Address the challenges brought on by an increasing student population enrolling in algebra. Hpot,Ball, Qback

99. Helping Students Succeed

100. Students not remembering Do it right on the first go around Take the time you need to more fully and appropriately develop concepts and skills Link concepts/skills to previously learned material & outside experiences

101. Student deficiencies To address student deficiencies: –Use the long term memory review –Use linkage when introducing new concept or skill

102. Make sure students understand the concept or skill before practicing

103. Use simple straight forward examples to clarify what you are teaching! Increase difficulty later.

104. Algebra Note taking

105. Solving Linear Equations Obj.To solve linear equations that are not in the ax + b = c format. Strategy:Take a problem you do not recognize and change into one you do recognize (ax + b = c) by using the Properties of Real #s

106. Ex. Solve 2(3x – 4) + 5 = 15 How does this problem look different from equations in the ax + b = c format? Answer- How can you get rid of the parentheses? Answer-

107. 2(3x – 4) + 5 = 15 6x – 8 + 5 = 15 Now what do you do to put the the equation in ax + b = c format? 6x – 3 = 15

108. Equation is now in ax + b = c format, how do you solve it? Answer – 6x = 18 x = 3

109. Guided Practice Give students an opportunity to solve one or two equations to ensure understanding

110. Ex.Solve for y. 6y + 2 = 2y + 34 How is this problem different? Answer- What do you have to do to write in ax + b = c format? Answer-

111. 6y + 2 = 2y + 34 6y + 2 – 2y = 2y + 34 – 2y 4y + 2 = 34 Now the equation is in ax + b = c format, what do you do next? Answer-

112. 4y + 2 = 34 4y = 32 y = 8 What Properties allowed you to subtract and divide both sides of the equation by the same numbers? Answer-

113. Guided Practice Provide students an opportunity to solve equations with variables on both sides of the equation.

114. Math Explain to students that you can’t make math harder, you can only make problems longer.

115. Solve for x.7(2x + 1) + 3 = 4x – 10 How is this equation different from the equations we have solved before? Answer- What’s the general strategy for solving these equations? Answer-

116. Solve for x. x/2 + x/3 = 10 How is this equation different from equations that we have solved before? Answer- How do we get rid of the fractions? Answer-

117. General Strategy Write the general strategy for solving linear equations that are not in ax + b = c format.

118. 3 rd Essential - Homework Page 117, 1- 33 odd OR

119. Homework Read Section 3.4, Solving Linear Equations Define:Distributive Property Addition Property of Equality Write an equation in ax + b = c format Write the Order of Operations How does D-Prop help you solve equations? Write a strategy for solving linear equations that are not in ax + b = c format Page 117, 1, 3, 7, 11, 12,13, 19, 21, 24, 29

120. Regular Reviews Short and long term

121. Time on Task

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

123. Kinds of Questions Directed Echo Cue Conceptual

124. 3rd Essential - Homework

125. Practice Guided Group Independent

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

127. Homework Page 270, 1–32 odd

128. 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, 3, 6, 7, 9, 12, 13, 14, 21,23, 31

129. 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, 3, 6, 7, 9, 12, 13, 14, 21, 23, 31

130. Reviews Recently taught material Long term review

131. Student Assessment

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

133. 1 + 4 1 3 = 7 12

134. 5 + 24 7 18 = 24 = 3 4 CD = 72 18 x 4 24 x 3 = 72 Reducing Method 18/24 = 3/4

135. 18 24 = 3 4 5 = 15 72 7 = 18 28 72 + 43 72

136. 4th Essential- Test Preparation Test what you say you value: Instruction – Assessment – Balance Cumulative Questions Practice Tests - Parallel construction Setting a Date

137. Testing Testing drives instruction

138. Tests Test Design –Design tests that encourage study. –Test what you say you value

139. Test Preparation Do you know what you are going to test your students on BEFORE you begin to teach a unit? Use the * System in notes for test prep

140. Practice Tests

141. Tests Monitor student learning

142. Memory Aids Help your students remember

143. 5th Essential - Tests Form A ~ Form B

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

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

146. This organization strategy leads to Transparency Credibility Trust

147. 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

148. KISS KISS

149. What are you willing to do?

150. Summary My Kid Standard Success on Success Model Simple straight forward examples Organize students for learning; “5 + 1” Demonstrate – think aloud It’s about you!

151. 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

152. 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

153. 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

154. 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.

155. 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.

156. 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?

157. 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?

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