Its one of the most important questions math teachers ask every day: how do we engage students in meaningful, enjoyable mathematics? In this webinar for the Adaptive Math Learning community, presenters Zachary Champagne, Researcher at the Mathematics Formative Assessment Project at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM), and Tim Hudson, former Math Curriculum Coordinator for Missouris Parkway School District, and DreamBoxs Senior Director of Curriculum Design, shared useful insights about the Mathematical Practices that will help deepen students understanding, enjoyment, and success in math class. Zachary and Tim discussed how to stop teaching tricks and instead engage students in thinking like a mathematician. They also shared insights about the power of formative assessment, the importance of uncovering students intuitive thinking, and how technologies such as adaptive learning can support the Mathematical Practices. Topics included: understanding equality and precision, observing students engaged in sense-making, and designing learning experiences that empower students to look for important mathematics. Additionally, Julie Benay, Principal of Malletts Bay School in Vermont, shared how her school implemented DreamBox and the outcomes they experienced. View the webinar to learn how to make math more engaging for your students.
1. Want to Engage Your Students? Engage Them in the Math Practices
2. Zachary Champagne Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) Email: firstname.lastname@example.org Twitter: @zakchamp Julie Benay Principal, Malletts Bay School, Colchester VT Email: BenayJ@csdvt.org Twitter: @CSDCommunity Moderator: Tim Hudson Senior Director of Curriculum Design, DreamBox Learning Email: email@example.com Twitter: @DocHudsonMath
3. Exit Slip on the First & Last Day of School: What is Mathematics? What do Mathematicians Do?
4. From a 5th grade teacher in NY: I had a lot of good people teaching me math when I was a student earnest and funny and caring. But the math they taught me wasnt good math. Every class was the same for eight years: Get out your homework, go over the homework, heres the new set of exercises, heres how to do them. Now get started. Ill be around. p. 55, Teaching What Matters Most, Strong, Silver, & Perini, 2001
5. Design Limitation They were so concerned with making sure we knew how to do every single procedure we never learned how to think mathematically. I did well in math but I never understood what I was doing. I remember hundreds of procedures but not one single mathematical idea. p. 55, Teaching What Matters Most, Strong, Silver, & Perini, 2001
6. Common Core State Standards for Mathematical Practice
7. Zachary Champagne Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) Email: firstname.lastname@example.org Twitter: @zakchamp
8. MFAS-CCSS Project Approximately 1300 K Geometry Tasks and Rubrics developed between 2011 2013 and are now available via CPALMS http://www.cpalms.org/Resource/mfas.aspx K 3; Algebra and Geometry Lesson Study Toolkits developed between 2011 2013 are now available via CPALMS
9. Mathematics Practice Standards These standards describe the varieties of expertise that mathematics educators at all levels should seek to develop in their students. [They] describe ways in which developing student practitioners of the discipline of mathematics increasingly ought to engage with the subject matter as they grow in mathematical maturity and expertise [K-12]
10. Elaborations The Elaboration Document can be downloaded at the following link: http://commoncoretools.me/2014/02/12/k-5- elaborations-of-the-practice-standards/
11. Math Practice One Make sense of problems and persevere in solving them.
12. What does laying ceramic tile have to do with making sense of mathematics?
13. 3 inches 4 inches 5 inches
14. Why Mathematics?
15. What is Sense Making in Mathematics?
16. 198 + 37 = ? Consider This Problem
17. How a fourth grade student may solve it
18. What About the Content Standards? 1.OA.6: Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 4 = 13 3 1 = 10 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
19. Consider This Context.. At one very lucky elementary school there were exactly 15 students in every class. At the school there were 19 classrooms. How many students attended the school?
20. Standard Algorithm 4 1 9 x 1 5 1 9 5 + 1 9 0 2 8 5
21. Partial Product Algorithm 1 9 x 1 5 (9 x 5) = 4 5 (10 x 5) = 5 0 (9 x 10) = 9 0 (10 x 10) = 1 0 0 2 8 5
22. The Standard to Achieve is Make Sense Which Makes More Sense? 1 9 x 1 5 (9 x 5) = 4 5 (10 x 5) = 5 0 (9 x 10) = 9 0 (10 x 10) = 1 0 0 2 8 5 4 1 9 x 1 5 1 9 5 + 1 9 0 2 8 5 Standard Algorithm Partial Products
23. DreamBox Learning Partial Products on the Number Line
25. Multiplying with Partial Products DreamBox Learning
26. Optimal Partial Products DreamBox Learning
27. Making Sense of the Algorithm Visually DreamBox Learning
28. Algorithm with Estimate First DreamBox Learning
29. Distributive Property with Variables DreamBox Learning
30. Math Practice Six Attend to Precision
31. What Does Precision Look and Sound Like in Mathematics? [Students] state the meaning of the symbols they choose, including using the equal sign consistently and appropriately.
32. The Equal Sign Children in the elementary grades generally think that the equal sign means that they should carry out the calculation that precedes it and that the number after the equals sign is the answer to the calculation. Children must understand that equality is a relationship that expresses the idea that two mathematical expressions hold the same value. Faulkner, K., Levi, L., & Carpenter, T. 1999
33. A Research Study Faulkner, K., Levi, L., & Carpenter, T. 1999
34. Common Core - Equality in K- 2 1.OA.7 Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false. For example, which of the following equations are true and which are false? 6 = 6, 7 = 8 1, 5 + 2 = 2 + 5, 4 + 1 = 5 + 2. 1.OA.8 Determine the unknown whole number in an addition or subtraction equation relating three whole numbers. For example, determine the unknown number that makes the equation true in each of the equations 8 + ? = 11, 5 = ? 3, 6 + 6 = ?. K.OA.3 Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g., 5 = 2 + 3 and 5 = 4 + 1).
35. Equality Read each equation aloud and say whether it is true or not true. Then say why you think so. 8 = 4 + 4 3 + 2 = 4 + 1 7 = 7 3 + 3 = 8
36. A First Graders View on Equality (Take 1 and 2)
37. Equality with Virtual Manipulatives DreamBox Learning
38. Thanks For Your Time! Zachary Champagne Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCR-STEM) Email: email@example.com Twitter: @zakchamp Formative Assessment Tasks: www.cpalms.org/Resources/mfas.aspx
39. Using Adaptive Learning Technology to Support Mathematical Development Julie Benay Principal Malletts Bay School Colchester Vermont Email: BenayJ@csdvt.org Twitter: @CSDCommunity
40. About Malletts Bay School On the shores of Lake Champlain, minutes from Burlington Public school district of about 2,000 students Five Buildings Two K-2 Schools Malletts Bay School (PreK and 3-5) 1 Middle School 1 High School. Malletts Bay divides the community into distinct areas. District Hallmark Leadership in implementing differentiated instruction
41. Malletts Bay Students Many of our families live in Colchester & work elsewhere High percentage of divided or single parent families Over the past 10 years, grown to nearly 40% of students who qualify for Free or Reduced Price Lunch Small, but growing, population of English Learners because Colchester is close to the Vermont Refugee Resettlement Center ~17% of our students qualify for special education or a Section 504 plan. Majority of our families have Internet access
42. Math at Malletts Bay School CCSS-based Curriculum Core program: Everyday Math (EDM) All teachers follow a District pacing guide for EDM Each unit of EDM focused on a big idea aligned with standards and using supplemental resources Locally designed assessments determine the focus of instructional planning in each classroom Workshop model enables teachers to focus on instructing small groups of students based on learning needs Our District employs one math coach who works across the three elementary settings with 45 teachers. When we began using an adaptive math program (DreamBox), we did not have a Title I funded math intervention program.
43. Math Achievement For the past three years, we have exceeded Vermont state average Vermonts No Child Left Behind (NCLB) test has been the New England Common Assessment (NECAP). We meet Adequate Yearly Progress for All students We are Identified for: subgroups of students with disabilities particularly concerning, with only about 1/3 of students meeting the standard Subgroups of students from lower income homes
44. Access to Technology At MBS All classrooms have at least four devices: laptops netbooks desktops Students access DreamBox in the classroom during independent practice or skills time. Small dedicated mini-lab reserved for students on IEPs to access specialized programs 21 Classrooms share 1 laptop cart and 1 ipad cart WiFi throughout the building. All classrooms have an interactive whiteboard.
45. Sample Daily Schedules TIME Teacher A TIME Teacher B 8:30-8:40 Attendance and announcements 8:30-8:40 Attendance and announcements 8:45-9:30 Unified Arts (PE, Music, Art, etc) 8:40-9:10 Math Intervention 9:30 10:25 Writing/Word Study 9:10-10:10 Math Instruction 10:25-11:25 Math 10:10-11:05 Writing/Word Study 11:25-11:45 Math Intervention 11:10-11:50 Lunch/Recess 11:50-12:30 Lunch/recess 11:50-12:40 Science or Social Studies 12:30 1:25 Science or Social Studies 12:40-1:40 Reading Instruction 1:25-2:25 Reading Instruction 1:40-2:10 Reading Intervention
46. Adaptive Learning at MBS We learned about DreamBox through a workshop attended by one of our special educators After exploring the program (playing in the sandbox) and talking with DreamBox, we purchased a limited number of seats for students with disabilities in grades K-5 All special educators attended a free training session to learn how to: manage rosters utilize and interpret the rich data provided by the software. Parents were engaged through DreamBox parent letters All students assigned a seat in the program had access both at home and at school
47. Early Feedback We saw results immediately The process of placing students in the program: gave us good information about critical gaps in the learning progression helped us tailor instructional support in the classroom and in special education instructional sessions. Students really enjoyed DreamBox. Other programs we used required a great deal of practice and repetition, and students resisted being assigned to use them Conversely, students looked forward to using DreamBox and did not want to sign off when their sessions ended! DreamBox provided learning experiences well matched to students development of mathematical thinking. Students are provided with just enough challenge to keep the sessions interesting, and subtle prompts and direction for strategies when they were stuck. Students are engaged by the games personalizing their rooms.
48. Adaptive Learning in the Math Workshop Once other students in the classroom observed their peers using DreamBox, they asked if they could have access! Our K-5 team considered the results of DreamBox We are now working to implement a math workshop model that will allow teachers time to balance whole group instruction with small guided math groups. Our workshop model encourages the use of the eight Math Practices so key to the Common Core math standards. We have expectations for instruction to ensure that the adaptive learning program supplemented instruction, not replacing it Ongoing data updates are shared among teachers, special educators, and parents to ensure coordinated efforts to help students grow in their mathematical thinking and achievement.
49. Math Workshop Model: Malletts Bay School Part I: Mini-lesson (Full Class) Post learning target Warm up: Mental Math, Math Message Direction Instruction: Big Ideas Guided practice and gradual release (modeling, partner work, small groups) Part II: Small groups and Independent Practice (connected to Big Idea) May include: Teacher led small groups Planned, differentiated stations (games, problem solving) Pairs, student-led groups Seatwork and independent practice (Everyday Math math boxes) Part III: Summary and Closing (Full Class) Questions, comments, observations Reflections, exit tickets Homework explanation Part IV: Intervention (Additional Dedicated Practice) May include: Additional practice related to this lessons Big Idea Practice with basic facts and skills Enrichment Dedicated time for students to leave for supplemental or specialized instruction
50. Tiers of Support & Universal Access Our school uses a tiered model of support. A key feature is to ensure that all students benefit from first instruction in grade level standards. To accomplish this, we set aside a specific time in the daily schedule for supplemental instruction. Students who leave the classroom for Tier II or Tier III instructional support leave during these periods. We see the potential for DreamBox to serve as an engaging and perfectly tailored anchor activity within our workshop model. With an eye toward prevention, we used DreamBox with students who were having difficulties in math but who were not identified as needing special education. Beginning in 2014, all students K-5 will have access to this adaptive learning program.