Aligning Curriculum to Math Standards: An Overview of the New Mathematics Benchmark Toolkit
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1 Aligning Curriculum to Math Standards: An Overview of the New Mathematics Benchmark Toolkit Superintendents Conference August 9, 2016 Beth Aune Director of Academic Standards and Instructional Effectiveness Sue Wygant Mathematics Specialist
2 A Quest for Deeper Understanding Goals To understand the purpose of the Toolkit To consider possibili4es for how the Toolkit can help you improve math achievement in your school or district Agenda Toolkit overview Math performance: Statewide findings Examples of school or district benchmark reports Moving Forward Connec4ons to messages in Coherence 2
3 The Mathema*cs Benchmark Toolkit A resource that was created to help educators focus their efforts for improved mathema4cs achievement. Provides state-level data about the difficulty levels of the mathema4cs benchmarks and a suggested process for using the state data along with school and district benchmark reports to help educators iden4fy concerns and areas for improvement. MCA overall MCA strand MCA benchmark 3
4 The Mathema*cs Benchmark Toolkit hhp://goo.gl/ylcgnd From the MDE Website (educa4on.state.mn.us): Educator Excellence > Standards, Curriculum and Instruc4on > K-12 Academic Standards > Mathema4cs 4
5 Contents of the Mathema*cs Benchmark Toolkit Overview of the Mathema*cs Benchmark Toolkit How to Use the Mathema*cs Benchmark Toolkit 2007 Minnesota K-12 Academic Standards in Mathema*cs by Grade with Benchmark-Item Difficulty Coding 5
6 Example of a Grade Level Snapshot 6
7 Contents of the Mathema*cs Benchmark Toolkit Overview of the Mathema*cs Benchmark Toolkit How to Use the Mathema*cs Benchmark Toolkit 2007 Minnesota K-12 Academic Standards in Mathema*cs by Grade with Benchmark-Item Difficulty Coding 2007 Minnesota K-12 Academic Standards in Mathema*cs by Progression with Benchmark-Item Difficulty Coding 7
8 Example of a Progression Snapshot 8
9 Contents of the Mathema*cs Benchmark Toolkit Overview of the Mathema*cs Benchmark Toolkit How to Use the Mathema*cs Benchmark Toolkit 2007 Minnesota K-12 Academic Standards in Mathema*cs by Grade with Benchmark-item Difficulty Coding 2007 Minnesota K-12 Academic Standards in Mathema*cs by Progression with Benchmark-item Difficulty Coding Grade Level Templates School/District Template 9
10 Coding for State Benchmark-item Difficulty Levels IMPORTANT NOTE: This coding does not indicate that the mathema4cs is more or less difficult; it indicates how students are doing with the content. 10
11 Mathema4cs Standards 11
12 Statewide Findings: Grade 4 Benchmarks , , and are among the least challenging benchmarks. These benchmarks are about single- and mul4-digit mul4plica4on. Benchmarks , , and are among the least challenging benchmarks. These benchmarks are about angles, area of a rectangle, and reflec4ons. 12
13 Statewide Findings: Grade 4 Frac4on and decimal computa4on benchmarks are among the benchmarks with average difficulty, but the benchmarks involving frac4on and decimal representa4ons and rela4onships ( , , , ) are among the most difficult. Benchmark (describing and classifying quadrilaterals) is one of the most challenging benchmarks. While benchmark is among the least challenging, benchmark which involves using this knowledge for figures that can be decomposed into rectangles, is among the most difficult. 13
14 MN Mathema*cs Progressions 14
15 Statewide Findings in Geometry: Measurement Nearly all measurement benchmarks involving area and volume are among the most difficult benchmarks for the given grade level. This can be seen beginning with the area of figures that can be decomposed into rectangles ( ) in 4th grade to figures that can be decomposed into triangles ( ) and volume and surface area of rectangular prisms ( , ), in 5th grade to surface area and volume of prisms ( ), area of any quadrilateral ( ), and es4ma4ng perimeter ( ) in 6th grade to volume and surface area of cylinders ( ) in 7th grade to distance ( ) in 8th grade to surface area and volume of pyramids, cones, and spheres ( , ) in high school.
16 Content Videos Spanning K HS Composing and Decomposing in Geometry Algebra and Representa4ons Proper4es and Computa4on Measurement and Frac4ons 16
17 Composing & Decomposing in Geometry KINDERGARTEN K No*cing Shapes 1 st Grade Decomposing Shapes 2 nd Grade Sor*ng Shapes 3 rd Grade Parallel and Perpendicular Lines 4 th Grade Composing for Area
18 Composing & Decomposing in Geometry 5 th Grade Area of a Triangle 6 th Grade Area of a Kite 18
19 Composing & Decomposing in Geometry 7 th Grade Circles 19
20 Composing & Decomposing in Geometry 8 th Grade Pythagorean Theorem 20
21 Composing & Decomposing in Geometry Area = b 2 a 2 High School Area of a Regular Octagon 21
22 Composing & Decomposing in Geometry High School Area of a Regular Octagon
23 School/District Benchmark Reports The purpose of the benchmark reports is to help iden4fy possible gaps in instruc4on. A benchmark report focuses on varia4on within a school or district benchmark data is rela4ve to the expected performance for the school it does not allow for comparisons between schools. Frame interpreta4on of the benchmark report in the context of the school s environment. Experience with the math curriculum, instruc4on, and data from classroom assessments is cri4cal to making meaningful inferences from this report. Though available in Reading, Science, and Math, there are differences in the benchmark reports for each subject area due to the type of test given. We are only looking at math today! 23
24 4 th Grade District Benchmark Report 24
25 District Performance by Benchmark Benchmark Code State Reference Line Overall Performance Expecta*on Performance marker for Benchmark Common Language Effect Size (CLES)
26 District Performance by Benchmark For individual benchmarks, comparisons are made between school performance (markers) and expected school performance (dashed ver4cal line)-not state performance Green Square Students performed significantly above expecta4on Blue Triangle Students performed near expecta4on Red Circle Students performed significantly below expecta4on 26
27 Two Strands from Two 8 th Grade Benchmark Reports Site A Site B
28 Some Ques*ons to Consider Does the district/school Benchmark Report data mirror what is happening in classrooms? Are there gaps in the alignment of the curriculum to the standards and benchmarks? If the curriculum is aligned to the standards and benchmarks, how are we ensuring that the curriculum is being taught as intended? (Are we sure that all students are receiving instruc4on on all benchmarks?) Do students receive instruc4on in all of the benchmarks before the MCA-III is given? What data are collected at the local level to monitor achievement on the standards and benchmarks? 28
29 Some Ques*ons to Consider How do teachers record progress toward the standards and benchmarks? What collabora4ve structures are in place to support adult learning of mathema4cs content, learning trajectories, and different instruc4onal responses to student thinking? Are beliefs about mathema4cs or beliefs about learners causing lower expecta4ons, narrower curriculum, and remedial tracks? Is there an overemphasis on learning procedures without connec4ons to meaning, conceptual understanding, and the applica4ons of mathema4cs that require these procedures? Is there sufficient ahen4on to mathema4cal problem solving, representa4ons, and reasoning, or do learning experiences and assessments emphasize skills and factual recall? 29
30 How to Use the Mathema*cs Benchmark Toolkit Review State Level Benchmark-item Difficulty Data 2007 Minnesota K-12 Academic Standards in Mathema*cs by Grade with Benchmark-item Difficulty Coding 2007 Minnesota K-12 Academic Standards in Mathema*cs by Progressions with Benchmark-item Difficulty Coding Review School/District Benchmark Reports Grade Level Templates School/District Template Other Classroom/School/District Data Achievement Level Descriptors Minnesota Math & Science Frameworks scimathmn.org/stemtc 30
31 Key Strategies to Consider Bundle or cluster the benchmarks across strands to maximize the coherence of mathema4cs instruc4on within each grade level. For example, the elementary benchmarks in the Algebra strand support the benchmarks in the Number and Opera0on strand and encourage students to develop conceptual connec4ons for procedures. These connec4ons are cri4cal for student achievement in mathema4cs. Consult the Achievement Level Descriptors. Use the Mathema4cs and Science Frameworks. 31
32 Achievement Level Descriptors Achievement Level Descriptors (ALDs) describe the four levels of achievement on the Minnesota Academic Standards. For each strand in each grade, what does achievement look like at each level: Does Not Meet Par4ally Meets Meets Exceeds MDE > Educator Excellence > Tes4ng Resources > Achievement Level Descriptors 32
33 Minnesota Mathema*cs and Science Frameworks 33
34 MDE Math Resources & Ini*a*ves Benchmark Toolkit Math Anima4on Videos Math and Science Frameworks Midwest Comprehensive Center Resources (under development) On MDE Calendar MN Math Leaders Networking sessions Math Webinars Coaching session with Lucy West Sept 19 Symposium April 27 Math Tiered Fidelity Inventory Math & Science Partnership MN Standards Portal (under development) Regional Centers of Excellence Math Task Force Teacher Analysis of Student Thinking 34
35 Aligning Curriculum to Math Standards: An Overview of the New Mathema*cs Benchmark Toolkit Superintendents Conference August 9, 2016 Beth Aune Sue Wygant 35
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