Assessment FOR learning In the 3 rd grade everyday mathematics classroom

1. Assessment FOR learning In the 3rd grade everyday mathematics classroom Kari Backhaus

2. The Philosophy of Everyday Mathematics • “Everyday Mathematics assumes that virtually all students are capable of a much greater understanding of, and proficiency in mathematics than has traditionally been expected. The program establishes high expectations for all students and gives teachers the tools they need to help students meet, and often exceed, those expectations. Everyday Mathematics is committed to establishing world-class mathematics standards for our nation’s schools” (p. 4). • Bell et al. (2004b)

3. Everyday Mathematics Overview Lessons are divided into 3 parts: • Teaching the Lesson: This section contains the main instructional activities for the lesson. This is where most new content is introduced. • Ongoing Learning and Practice: This section provides materials and suggestions for essential review, practice, and maintenance activities. • Options for Individualizing: This section includes activities for re-teaching, extra skill practice, enrichment, and meeting the needs of particular populations (ESL, etc). These suggested activities relate directly to the main instructional activities in Part 1 of the lesson.

4. Everyday mathematics General Rubric • Beginning (B) Children cannot complete the task independently. They show little understanding of the concept or skill. • Developing (D) Children show some understanding. However, errors or misunderstandings still occur. Reminders, hints, and suggestions are incorporated with understanding. • Secure (S) Children can apply the skill or concept correctly and independently. • Side Note: MPSD Elementary Reporting

5. Lesson components • Math Messages • Mental Math and Reflexes • Math Boxes • Games • Home Links • Checking Progress

6. Math Messages A Math Message is provided at the beginning of each lesson and usually leads into the lesson for the day or reviews topics previously covered. Children should complete the Math Message before the start of each lesson.

7. Mental Math and Reflexes The term Mental Math and Reflexes refers to exercises, usually oral, designed to strengthen children's number sense and to review and advance essential basic skills. Mental Math and Reflexes sessions should be brief, lasting no more than five minutes. Numerous short interactions are far more effective than fewer prolonged sessions.

8. Math Boxes Math Boxes are an excellent way to review material on a regular basis. They are one of the main components of review and skills maintenance. Math Boxes problems are not intended to reinforce the content of the lesson in which they appear. Rather, they provide continuous distributed practice of all skills and concepts in the program. The Math Boxes page does not need to be completed on the same day as the lesson, but it should not be skipped. These are designed as independent activities.

9. Games Games are enjoyable ways to practice number skills; especially those that help children develop fact power. Games are an integral part of the program, rather than an optional extra as they are traditionally used in many classrooms. Games can also be played frequently without the same mathematical problems repeating because the numbers in most games are generated randomly. The game format eliminates the tedium typical of most drills.

10. Home Links Home Links are the Everyday Mathematics version of homework assignments. Each lesson has a Home Link. The next lesson has a follow-up to the previous Home Link. Home Links consist of active projects and ongoing review problems that show parents what the children can do in mathematics. Home Links activities serve three main purposes: They (1) promote follow-up, (2) provide enrichment, and (3) involve parents or guardians in their children's mathematics education. Everyday Mathematics also provides Family Letters that are meant to be sent home at the with particular Home Links. These letters explain an idea or an activity that parents might not be familiar with.

11. Checking progress Summative assessments included in the Everyday Mathematics program

12. Complaints about current program • Teachers: • “It’s definitely not as hands-on or real-world based as Investigations!” • Parents: • “The algorithms taught in the program are completely different from the way I learned. I can’t even help my kid with his homework!” • Students: • “I’m bored! It’s the SAME thing everyday. I’m never going to use this stuff anyway.”

13. The problem: The Challenge • Minimal new-teacher training of Everyday Mathematics and Authentic Intellectual Achievement (portfolio process) • No significance placed on importance formative assessment has on instruction. • Assessment suggestions located across three manuals: Teacher’s Manual, Assessment Handbook, and Teacher’s Reference Manual • 21st century learners need assessments that require them to utilize skills relevant to their world

14. The problem: the solution • Analyze current EM formative/summative assessments and revising and/or creating new formative and summative authentic-based assessments using Authentic Intellectual Achievement rubric • Organize formative and summative assessment suggestions into one document by unit and lesson • Offer online-support for parents to help students at home • Incorporate student-involvement and self-reflection in the process • Train new and old teachers about importance of formative assessment and authentic work!

15. Behind the scenes- red flag • Personal experiences with Everyday Mathematic assessment has shown little real-world integration. • Decided to survey fifth grade math teachers in the MPSD to get an overall scope of teacher attitudes of current summative assessment practices • Fifth Grade Teacher Evaluation of Summative Assessments

16. WKCE 2008-2009 Results • WKCE Results- MPSD • Why is Mathematics one of the weakest areas in the MPSD? • Why is Social Studies one of the strongest areas in the MPSD? • Possible solution: Need more real-world based math exposure!

17. Why is this important? • In order to prepare students for a competitive global economy: • our 21st century learners need to be equipped with problem-solving and reasoning skills • Find practicality of math instruction in which connections can be made • Clearly and elaboratively communicate their thinking • Synthesize and hypothesize to produce new understandings that can be taken beyond the classroom • Demonstrate math procedures used by adults and experts in mathematical fields

18. Obstacles of the plan • Inaction of teachers • Students continue as is- minimal real-world mathematical exposure • Missing formative assessment piece = overachieving/underachieving student needs not met • Disconnect • Teachers who do not teach authentically may have difficulty assessing authentically • Resources • Lack of internet access for parents • School Networking Issues for teachers

19. Supporting data • Formative assessment • Assessment tools • Authentic Intellectual Achievement • Home-school connection

20. Formative AssessmentWhy it’s beneficial

21. Formative vs. summative AssessmentJ. Dodge and R. Stiggins (2009, 2007) • Summative Assessments • Assessments OF learning • Given after a period of time to check how much learning has taken place • Traditional assessments • Formative Assessments • Assessments FOR learning • Check for understanding along the way • Guides teacher instruction • Provides feedback for students to improve performance

22. Formative AssessmentO’Conner (2002) • Black and William (researchers) looked at a large number of studies done over a ten year period and discovered strong evidence that formative assessment leads to student achievement gains. • Formative assessment were especially beneficial for low achievers which have shown to reduce the achievement gap while raising overall achievement for all student.

23. Formative AssessmentHow to do it

24. Formative Assessment Strategies • Dry erase/slate assessments Dodge (2009) and Bell et al. (2004) • Math Box Cover-upBell et al. (2004) • 3-2-1 Summarizer (aka Exit Tickets)Dodge (2009) • 3 Things you learned (knowledge) • 2 Questions you have (application) • 1 Connection you make (synthesis)

25. Formative Assessment Recording Tools • Observational Checklists • Flip-Card Tools

26. Authentic Intellectual Achievement

27. The authentic evaluation modelNeumann and Wehlage (1993) • Three major components • Disciplined Inquiry • Students show understanding and demonstrate methods used by experts in the field and communicate their findings elaboratively in oral, symbolic or written fashions. • Value Beyond School • Students address problems similar to ones outside of school and direct performances to someone other than the teacher. • Construction of Knowledge • This requires students to interpret, synthesize and evaluate complex information using higher-order thinking.

28. Self-ReflectionBrookhart (2008) • Tests are full of information that never gets used because students care more about the grade. When students are taught how to analyze their test results and know they’ll get a chance to use the feedback on the test, test results can be a gold mine (p. 66) • Self-Reflection after summative assessment

29. The power of portfolios(Bell et al., 2004a, Stiggins, 2001, Wiggins & McTighe, 1998) • Prioritizing, planning, managing and self-direction are significant components of 21st century learner skills that can be achieved through a portfolio process. • Portfolios also involve children more directly in the assessment progress. Children take responsibility to write introductions and help select portfolio entries they are proud of and explain why they chose each piece. • Portfolios can also illustrate children’s strengths and weaknesses in particular areas of mathematics and be used to assess children’s abilities to reveal connections within mathematics and to apply mathematical ideas to real-world situations

30. The power of portfolios(Bell et al., 2004a, Stiggins, 2001, Wiggins & McTighe, 1998) • Provides a venue for students “to take notice of, keep track of, and celebrate their learning” and collect and organize and reflect on their own work. This builds an understanding of students as learners and can nurture a sense of accomplishment. • Lead to Student-led conferences

31. Clear expectations for successStiggins, R., Arter, J., Chappuis, J., & Chappuis, S. (2007) • Learning targets need to be clear and understandable in kid-friendly language • Students are involved in developing criteria for quality work • Anonymous examples of weak and strong student work should be used as models for expectations for success (p.30) • A teacher model should be created/used for example of high-quality work

32. Support– for teachers, parents and students Algorithm Demonstrations and NCTM Standard Correlation Charts • https://www.everydaymathonline.com/ Third Grade Everyday Math Games (by lesson) • http://www1.center.k12.mo.us/edtech/edm/3.htm Math Box and Learning Target Alignments • http://www.westseneca.wnyric.org/West_Seneca_Web_Pages/west%20elem/teacher/Beth%20Ribbeck/everyday%20math/math%20boxes%20for%20grade%205.pdf

33. Educational philosophy: Progressivism and social reconstructivism • Progressivist: John Dewey • “Learning should be directly related to the interests of the child.” • Authentic-based assessments are imbedded in real-world contexts that students can connect to and use beyond the classroom • “Students should be involved in their learning.” • Students are often asked to self-reflect on assessments, in-class activities and understandings, and portfolio entries. • High-quality work criteria is created with student input

34. Educational philosophy: Progressivism and social reconstructivism • Social Reconstructivist: John Childs • “Learning focuses on solving real societal problems.” • When students are required to use higher-order thinking skills, access deep knowledge, and address problems and issues similar to ones they will encounter outside of the classroom, students are given opportunities to be real-world problem-solvers. These are critical skills required of 21st century learners.

35. 21st century skills

36. Curriculum Evaluation Plan: assessment activity • Use the Authentic Intellectual Achievement Rubric to evaluate Everyday Mathematics • Unit 1 Checking Progress • Stretch your legs and post your evaluations on the Authentic Assessment posters

37. Checking progress Summative assessments included in the Everyday Mathematics program

38. Standards-based resource Wisconsin State Standards • https://www.wrightgroup.com/download/em/g3_wi_reverse.pdf NCTM Standards (National Mathematics Standards) • https://everydaymath.mhlgt.com/pdf/teacher/focal_points/Grades_Pre-K_-_6_Correlations/Grade_3_Correlation_pp_43-47.pdf

39. 3rd Grade teacher attitude survey • Third Grade Cover Letter • Third Grade Teacher Assessment of Current Mathematics Assessments • This survey serves two purposes: • To inform me how teachers feel math assessments are represented authentically • To give teachers a heads up that third grade math assessment is being evaluated and revised

40. Curriculum plan, Timeline, and evaluation • Curriculum Plan, Timeline, and Evaluation Process • Assessment Evaluation Rubric

41. Assessment materials • Assessment Overview • Unit Checklist(used for formative assessment recording tool) • Learning Goal Poster • Authentic-based Summative Assessment – fifth grade example • Self-Reflection of Summative Assessment – fifth grade example