1. C Extending Mathematical Power with Date Name

2. Introduction to EMPower Math State of Numeracy in the US Current (and Future) Shifts in Adult Ed The EMPower Classroom: Connecting Standards to Practices Next Steps – EMPowering Your Students! Agenda

3. “They know some of the steps to solve a problem but then get confused. It reveals that they, at some point, learned a procedure/formula, but don’t really understand how the numbers relate to each other and why that formula/procedure works.“ The heart of the issue… https://community.lincs.ed.gov/discussion/piaac-have-we-reached-numeracy-crisis-us

4. 4 Introduction to EMPower Math

5. 5

6. Developed and piloted over the course of four years (2000-2004) Designed for students who return for a second chance at education: o Adult basic education o High school equivalency o Developmental math programs Focus on competency in mathematical problem solving and communication Why EMPower Math?

7. EMPower asks learners to Work collaboratively with others on open- ended investigations Draw from their own life experiences Focus on application and concept before procedure Develop their confidence in becoming self- directed, performance-centered learners A Focus on Andragogy

8. 8 State of Numeracy in the US

9. Exam# Test Takers# Completers % Passers GED® Test223,000140,00062.8% HiSET® Exam50,00031,00062% TASC Test43,00025,00058% High School Equivalency Pass Rates Source: NCSDAE (March 2015)

10. TASC Test™ “Of the five content areas that passers took multiple times in order to pass, there were more retakes of the Mathematics test compared to any other content area.” Source: TASC Test 2014 Annual Statistical Report (2015). Data Recognition Corporation. From the Testing Providers…

11. GED® Test Source: GED® Testing Service, April 2015. From the Testing Providers… SubjectPass Rate Language Arts77% Mathematics60% Science75% Social Studies71%

12. HiSET® Exam From the Testing Providers… Source: 2014 Annual Statistical Report on the HiSET® Exam. (2015) Educational Testing Service

13. Survey of Adult Skills (Oct 2013) Sources: http://www.oecd.org/site/piaac/PIAAC%20Framework%202012--%20Revised%2028oct2013_ebook.pdf http://www.oecd-ilibrary.org/education/time-for-the-u-s-to-reskill_9789264204904-en

14. How did US performance compare? 16 th of 24 countries 22 nd of 24 countries

15. 15 LiteracyNumeracyPS in Tech Rich JapanFinland NetherlandFlanders-BelgiumAustralia NetherlandsSweden Norway Netherlands EstoniaDenmarkAustria Flanders-BelgiumSlovak Rep.Denmark Czech Rep. Slovak Rep.AustriaKorea, Rep. of CanadaEstoniaGermany Korea, Rep. ofGermanyCanada United KingdomAustraliaSlovak Rep. DenmarkCanadaFlanders-Belgium GermanyCyprusUnited Kingdom United StatesKorea, Rep. ofEstonia AustriaUnited KingdomUnited States CyprusPolandIreland PolandIrelandPoland IrelandFranceItaly FranceUnited StatesSpain ItalyCyprus ItalySpainFrance LiteracyNumeracyPS in Technology -Rich Japan Finland NetherlandFlanders-BelgiumAustralia NetherlandsSweden Norway Netherlands EstoniaDenmarkAustria Flanders-BelgiumSlovak Rep.Denmark Czech Rep. Slovak Rep.AustriaKorea, Rep. of CanadaEstoniaGermany Korea, Rep. ofGermanyCanada United KingdomAustraliaSlovak Rep. DenmarkCanadaFlanders-Belgium GermanyCyprusUnited Kingdom United StatesKorea, Rep. ofEstonia AustriaUnited KingdomUnited States CyprusPolandIreland PolandIrelandPoland IrelandFranceItaly FranceUnited StatesSpain ItalyCyprus ItalySpainFrance

16. US “Less-than-basic” Levels 1 in 61 in 3 Roughly 36 million adultsDifficulty beyond counting, basic computation, & sorting Source: Organisation for Economic Co-operation and Development, Survey of Adult Skills (PIAAC) (2012).

17. Scores of PISA (2006) Compared to Survey of Adult Skills (2012) Source: OECD, Survey of Adult Skills (2012) and OECD, PISA databases (2000, 2006)

18. Literacy vs. Numeracy https://adultnumeracyatterc.wordpress.com/2015/05/08/46/

19. Focus on doing, not thinking (No Child Left Behind, Race to the Top) Interruption of the conceptual continuum Need to get into a job as fast as possible Lack of instructor training and professional development Emphasis on basic skills and diagnostics, not on true mathematical proficiency How did we get here?

20. Topic 1 Topic 2 Topic 3 Topic 4 Topic 5 Topic 6 Topic 7 1. Diagnose 2. Address gaps (drill & kill) 3. Retest HSE Preparation – “Diagnose & Fix”

21. Sally has five apples and four oranges. How many bananas can she trade these for? This is the result…

22. 22 Current (and Future) Shifts in Adult Education

23. Source: Pimentel, Susan. College and Career Readiness Standards for Adult Education. MPR Associates, Inc. April 2013. Source: www.corestandards.org CCRS Standards for Adult Education

24. . 10 anchor standards 8 mathematical practices Grade-specific standards for grades K - 12 Levels across GLE spans: A: K – 1 B: 2 – 3 C: 4 – 5 / 4-5, +6 D: 6 – 8 / +6, 7-8 E: 9 - 12 CCSS & CCRS Key Comparisons

25. Integration of the CCRS assumes… Goal is to prepare adult education students for postsecondary training without needing remediation. Each standard identifies beginning levels of study, reaching students at their instructional levels upon program entry and positioning them for successful progress toward college and career readiness. CCRS Assumptions

26. “At the heart of these shifts is a focus in mathematics instruction on delving deeply into the key processes and ideas upon which mathematical thinking relies.” From the standards… Source: U.S Department of Education, Office of Vocational and Adult Education. College and Career Readiness Standards for Adult Education. Washington, D.C., 2013

27. Shift 1 – Focus Focus strongly where the standards focus Shift 2 – Coherence Designing learning around coherent progression level to level Shift 3 – Rigor Pursuing conceptual understanding, procedural skill & fluency, and application – all with equal intensity Key Shifts in Mathematics

28. LevelFocus Level A (K – 1)Number Sense, Algebra, Geometry Level B (2 – 3)Number Sense, Measurement & Geometry Level C (4 – 5, 6)Number Sense, Algebra & Geometry, Data Analysis & Probability Level D (6, 7 – 8)Number Sense, Algebra, Geometry, Statistics & Probability Level E (9 – 12)Algebra & Number Sense, Algebra & Geometry, Statistics & Probability LevelFocus Level A (K – 1)Number Sense, Algebra, Geometry Level B (2 – 3)Number Sense, Measurement & Geometry Level C (4 – 5, 6)Number Sense, Algebra & Geometry, Data Analysis & Probability Level D (6, 7 – 8)Number Sense, Algebra, Geometry, Statistics & Probability Level E (9 – 12)Algebra & Number Sense, Algebra & Geometry, Statistics & Probability Shift 1: FOCUS Mile Deep, Inch Wide

29. Where SHOULD we focus?

30. Are we missing the mark? Source: National Council on Education and the Economy. What Does It Really Mean to Be College and Work Ready? The Mathematics Required of First Year Community College Students. Washington, D.C., 2013

31. Are we missing the mark? Source: National Council on Education and the Economy. What Does It Really Mean to Be College and Work Ready? The Mathematics Required of First Year Community College Students. Washington, D.C., 2013

32. Are we missing the mark? Source: National Council on Education and the Economy. What Does It Really Mean to Be College and Work Ready? The Mathematics Required of First Year Community College Students. Washington, D.C., 2013

33. PreK-2 3-5 6-8 9-12 Number Algebra Geometry Measurement Data Analysis & Probability Shift 2: COHERENCE Planning is Everything

34. GED ® Test HiSET ® Exam TASC Test Numbers & Operations Geometry & Measurement Statistics & Probability Quantitative Problem Solving Algebra Functions 55% 65% 64% HSE Test Comparison

35. We’re aligned! Alignment: A Love Story

36. The CCRS are a subset of the CCSS ALL three tests have standards that are aligned to the CCRS and CCSS NONE of the tests fully cover the CCRS or CCSS (at the moment) What “Alignment” Means

37. New NRS ABE/ASE levels coming (Spring 2016) These levels will be CCRS aligned New NRS tests used for EFL gains (TABE, CASAS, GAIN, MAPT) will be aligned to the new NRS levels (timeframe TBD) And more shifts to come…

38. Level Descriptors Beginning ABE Literacy Individual has little or no recognition of numbers or simple counting skills or may have only minimal skills, such as the ability to add or subtract single digit numbers. Beginning Basic Individual can count, add, and subtract three digit numbers, can perform multiplication through 12, can identify simple fractions, and perform other simple arithmetic operations. Low Intermediate Basic Individual can perform with high accuracy all four basic math operations using whole numbers up to three digits and can identify and use all basic mathematical symbols. High Intermediate Basic Individual can perform all four basic math operations with whole numbers and fractions; can determine correct math operations for solving narrative math problems and can convert fractions to decimals and decimals to fractions; and can perform basic operations on fractions. Low Adult Secondary Individual can perform all basic math functions with whole numbers, decimals, and fractions; can interpret and solve simple algebraic equations, tables, and graphs and can develop own tables and graphs; and can use math in business transactions. High Adult Secondary Individual can make mathematical estimates of time and space and can apply principles of geometry to measure angles, lines, and surfaces and can also apply trigonometric functions. Current NRS Numeracy Descriptors

39. What’s to Come… Current DescriptorProposed Descriptor Individual can perform with high accuracy all four basic math operations using whole numbers up to three digits and can identify and use all basic mathematical symbols. Number Sense and Operations: Students prepared to exit this level understand place value for both multi-digit whole numbers and decimals to thousandths, and use their understanding to read, write, compare, and round decimals. They are able to use their place value understanding and properties of operations to fluently perform operations with multi-digit whole numbers and decimals. They can find common factors, common multiples, and understand fraction concepts, including fraction equivalence and comparison. They can add, subtract, multiply and divide with fractions and mixed numbers. They are able to solve multi-step word problems posed with whole numbers and fractions, using the four operations. They also have an understanding of ratio concepts and can use ratio language to describe a relationship between two quantities, including the concept of a unit rate associated with a ratio. Low Intermediate Basic – Numeracy

40. Source: National Research Council Shift 3: RIGOR How to build proficiency

41. 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Mathematical Practices

43. 43 The EMPower Classroom: Connecting Standards to Practice

44. 1.Make sense of problems and persevere in solving them. 2.Reason abstractly and quantitatively. 3.Construct viable arguments and critique the reasoning of others. 4.Model with mathematics. 5.Use appropriate tools strategically. 6.Attend to precision. 7.Look for and make use of structure. 8.Look for and express regularity in repeated reasoning. Mathematical Practices

45. Literacy vs. Numeracy https://adultnumeracyatterc.wordpress.com/2015/05/08/46/

46. The EMPower classroom… emphasizes making connections across mathematical concepts activities that lead learners to “discover” the math. Interconnect Concepts & Skills

47. 8 + 4 (4 + 2) + (4 + 2) How Many Tiles? (2 x 4) + (2 x 2) 2 (4 + 2) =

48. How Many Tiles? Counting Composition/decomposition Basic operations Order of operations Concept of equality Area Basic algebra How are these concepts connected?

49. Careful Conceptual Progression From EMPower Plus - Everyday Number Sense Lesson 10: Picture This

50. Clear Facilitation From EMPower Plus - Everyday Number Sense Lesson 10: Picture This

51. Extensions 2 6 ?

52. Test Practice

53. Foster Learning Communities The EMPower classroom… Emphasizes a collaborative learning environment, allowing for learners to learn from other students through mathematical discourse, helping them internalize deeper understanding of the mathematics.

54. Challenges: Mathphobia Carefully thought out collaborative activities help overcome lagging confidence o Encourage divergent thinking o Promote discussion & mathematical discourse o Allow for success for various learner entry points Find x 6 cm 8 cm x

55. Multiple Levels = Multiple Perspectives 40 – 27 = ___ 1.How would you show this subtraction problem visually – such as with a picture or a diagram? 2.How would you connect that to a real-world situation? 3.Using the same numbers, think of another real-world situation to show another way to think about subtraction. From EMPower Plus - Everyday Number Sense Lesson 5: Meanings and Methods for Subtraction

56. Take-away Interpretation From EMPower Plus - Everyday Number Sense Lesson 5: Meanings and Methods for Subtraction 40 – 27 = ___ “I had 40 CDs in my collection, then gave 27 to my friend. How many do I have now? “

57. Comparison Interpretation 40 – 27 = ___ “I have 40 CDs. My sister has 27. How many more do I have than she does? “

58. Missing Parts Interpretation 40 – 27 = ___ From EMPower Plus - Everyday Number Sense Lesson 5: Meanings and Methods for Subtraction “This week I want to work a full 40 hours. I know that I still have 27 hours to go. How many hours have I already worked?” 40 = x + 27 How do I get from here: 40 – 27 = x to here:

59. The EMPower classroom… is built to allow for regular productive struggle, in which learners are allowed to take risks and engage divergent thinking as they approach problems, regardless of their entry points. Use Application to Lead to Process

60. Have you heard something similar? A student walks into their HSE test, opens up their test booklet, and sees a math problem on something that “you did not teach.” This causes the student anxiety, and he is unable to complete the math portion of the test. He does not pass.

61. Math should be PUZZLING Productive Struggle

62. How do we help our learners understand the tools they already have in their mathematical toolboxes? Strategic Competence

63. Changing the Culture: Active Learning Group Students: Match students whose learning styles and background knowledge complement each other. Allow Wait Time: Studies show that teachers often wait less than three seconds before asking another question. The GOAL? Help students learn to approach problems knowing there isn’t just one way; as long as they can figure out their way, they can arrive at a correct solution.

64. Changing the Culture: Communication Sit!: Watch students and allow them to struggle. Listen for logic and understanding. Follow and help guide students’ thinking to uncover unconventional approaches. Writing: Math journals and vocabulary journals help students demonstrate understanding and review and build upon what they have learned. The GOAL? Help students learn to reason through problems through mathematical discourse. More opportunity to explain reasoning deepens both confidence and understanding.

65. The EMPower classroom… develops concepts and skills within problems that have real-world contexts relevant to out-of-school youth and adult learners, because it was developed specifically with these populations in mind. Emphasize Math as a Lifelong Skill

66. Real-World Application Lesson 1: Countries in Our Closets from Many Points Make a Point: Data and Graphs Through gathering data about where their clothes were made, students: Use a frequency graph to organize data Identify the story data tell Compare data from various samples Articulate how changing how data is categorized changes the story

67. Real-World Application Establish Relevance

68. Real-World Application Identify the Story and Compare the Data

69. Real-World Application Articulate How the Story Changes

70. Real-World Application Lesson 2: Banquet Tables from Seeking Patterns, Building Rules: Algebraic Thinking

71. What Students Are Saying… “It’s more hands-on.” “More interesting.” “I use it in my life.” “We learn to work as a team.” “Our answers come from one another…[then] we work it out ourselves.” “I can help my children with their homework.” “MATH IS FUN!”

72. Updating the EMPower Series

73. The EMPower Plus Series NUMERACY, OPERATIONS SENSE, ALGEBRAIC REASONING DATARATIO/PROP ALGEBRA GEO/MEAS `

74. Operation Sense: More emphasis on the relationship between operations (doing and undoing) Equivalence: Much more emphasis on equivalence and balancing equations Stronger Connections: Moved operations instruction out of Operations Sense title and put it point of use within the Plus titles – making connections where it happens Accessible Language: Engaged experts to make the content more accessible to learners with different language backgrounds Why EMPower Plus?

75. Math Inspections Examine a notation or structure Name a pattern Test an idea EMPower Plus – What’s new?

76. EMPower Plus – Math Inspections Lianne says start with the biggest number, then the next largest, and so on. Peter says put the numbers in order from smallest to largest, then start at the top and work your way down. Ana says the order does not matter, just pay attention to what you are doing. Chen says take two numbers at a time and total them. Keep going until you have added everything. Ask students for each: Agree or disagree? Will this way always work?

77. EMPower Plus – Math Inspections

78. 78 Next Steps: EMPowering Your Students!

79. EMPower Plus – FAQs I have classes that are widely multi-level. Can this work? Turn this into an advantage Facilitate deep understanding by slowing down Make the Lesson Easier/Make the Lesson Harder

80. Use Technology!

81. Provide Additional Practice College & Career Readiness Practice Workbooks

82. EMPower Plus – FAQs How do I respond to comments such as “Can we go back to the old way?” Start small. Be clear about why they are doing this. Reiterate accomplishments and “Aha!” moments…celebrate success.

83. EMPower Plus – FAQs My own math background is not strong. Will I be able to teach this curriculum? Open-ended questions designed to keep conceptual development on track Lesson Commentary, Math Background, and Lesson in Action sections Professional Learning Environment (coming soon)

84. Professional Learning Environment Free for all EMPower Plus purchasers: Program QuickStart and overview modules for each unit Videos of actual EMPower practitioners describing their experiences Active discussion board to foster a community of practice Live April 2016

85. Additional Support Adult Numeracy Network (ANN) Conduct annual PD in conjunction with COABE and NCTM http://www.adultnumeracynetwork.org /index.html http://www.adultnumeracynetwork.org /index.html Adult Numeracy Initiative (ANI-PD) Series of three, two-day institutes http://lincs.ed.gov/professional- development/RPDC http://lincs.ed.gov/professional- development/RPDC

86. Teaching Core Standards in Adult Education Supporting Numeracy American Institutes for Research Adult Education PD Series

87. Teaching Core Standards in Adult Ed Assessing Adult Learner College and Career Readiness Supporting Adult Learner CCR in Operations & Algebraic Thinking Supporting Adult Learner CCR in Reading Supporting Adult Learner CCR in Writing Adult Education PD Series

88. Supporting Numeracy Adult Numeracy Assessment Adult Numeracy Communications & Connections Adult Numeracy Strand Integration & Connections Adult Mathematical Proficiency Adult Education PD Series

89. C Extending Mathematical Power with Sample Activity

90. SYNOPSIS Students explore ways to visualize and represent numbers and operations with arrangements of objects in arrays (rows and columns) and equal groups. This lesson is the first of two lessons that focus on totaling and breaking apart groups of items while making connections among visual representations, mathematical expressions and equations, and word problems. Lesson 10 Picture This

91. Mathematical Discourse From the teacher book… The class discusses ways to total items without individually counting each object. They record ideas using words and equations and by marking off arrays. Student pairs arrange collections of objects for ease in counting and write equations that reflect their arrangements. Students compare the algorithms they use to solve multiplication problems. Lesson 10 Picture This

92. Mathematical Connections From the teacher book… Individuals find at least two ways to record the total number of items in pictured groups, and then student pairs match equations with arrays. Using arrays, students make visible the subtotals resulting from the US standard algorithm. Students see the distributive property at work. Lesson 10 Picture This

93. Real-World Connections Lesson 10 Picture This From the teacher book… Student pairs solve the Garden Pathway problem, and the whole class reviews the problem. The class summarizes what they learned about showing equations and writing equations. Then they discuss using math to find totals in their daily lives.

94. Picture This – Opening Discussion

98. Why is it important to allow wait time in this question? The Difference

99. Picture This – Opening Discussion Why is it important to spend time looking at multiple approaches? The Difference

100. Picture This – Opening Discussion How does careful questioning promote accessibility for a range of learner levels? The Difference

101. Picture This – Opening Discussion Concepts introduced… Equivalent expressions Commutative property of multiplication Associative property of multiplication Multiple step computation Mathematical notation

102. Activity 1: Pictures & Numbers

104. 1. _______________________ 2._________________________ 3. ____________________________ 4. _________________________ Activity 1: Pictures & Numbers b. 10(11) + 3(11) d. 10 x 10 + 13 x 1 + 3 x 10 c. 10(10) + 10(1) + 3(10) + 3 (1) a. 13 x 10 + 13 x 1

105. Activity 1: Pictures & Numbers How does allowing for student struggle allow promote opportunities for various learner levels? How does it support communication & collaboration? The Difference

106. Through facilitation, Math Practices covered include… 1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of others. 4. Model with mathematics. 7. Look and make use of structure. 8. Look for and express regularity in repeated reasoning. Activity 1: Pictures & Numbers

107. This activity focuses on students finding efficient ways for counting large quantities, with an emphasis on: Justifying their reasoning Evaluating equivalent expressions What you do with “extras” (those that don’t fit into rows) Write expressions to represent pictures and draw pictures to represent expressions (and contextualizing it) Activity 2: Counting Smart

108. Activity 3: Garden Pathway

109. Examples conducive for showing how to simplify expressions: 10 + 10 + 10 + 10 + 14 + 1412 + 12 + 12 +12 + 10 + 10 Activity 3: Garden Pathway

110. Examples conducive for multiple steps/evaluating order of operations: 14 x 12 – 10 x 10 14(12) – 10(10) 14(12) – 10 2 Activity 3: Garden Pathway How does focusing on application first, then procedure, promote conceptual understanding? How can it help prevent test anxiety? The Difference

111. Up to this point, students have focused on looking at different ways to evaluate arrays. This has led to an understanding numbers can be written as expressions that combine multiple operations (composition and decomposition) This activity helps students arrive at the “why” behind the distributive property, which is the basis for our standard algorithm of multiplication Activity 4: Understanding the “Why”

112. Math Inspection: Angles, Arrays, & the Distributive Property

113. Math Inspection: Angles, Arrays, & the Distributive Property

114. 6 (4 + 3) = 6 x 4 + 6 x 3 6 x 7 = 6 x 4 + 6 x 3 5 (x + 3) = _____________ Math Inspection: Angles, Arrays, & the Distributive Property

115. Math Inspection: Connecting Arrays to Multiplication How does making mathematical connections help deepen students’ conceptual understanding? How does this benefit them on test day? Beyond? The Difference

116. Additional Student Practice Practice Group 1: Number of the Day (p. 168) Group 2: Carton of Eggs (p. 169) Group 3: Expressions, Arrays, & Stories (p. 170) Group 4: How do you see it? (pp. 171–172) Group 5: Stone Paths (p. 173 – 175) Group 6: Sketch the Two Expressions (p. 176) Mental Math Practice: Square Numbers Extension: Seeing Squarely & Missing Rolls Test Practice

117. Additional Student Tools

119. What have we covered? With a partner, list the concepts that were covered based on the lesson as it was facilitated today. Then, list at least 2 additional connections that could be made to enhance the lesson. Think about: o Connections to real-world concepts o Connections to other math concepts o Extensions of specific problems/activities

120. C Extending Mathematical Power with