Math Instructional Leadership Cadre Session 3 November 16 th and 18 th

Math Session 3 Fluency vs Algorithms Mathematical Practices 7 & 8 Balanced Assessment

Define Fluency

The Importance of Fact Fluency:  When students are unable to retrieve facts quickly and accurately, they have a higher cognitive load.  This leads to inefficient processing strategies (i.e., counting on fingers), which can lead to computation errors.  Math skills build upon one another, so by having automatic retrieval of facts, students are able to quickly solve more complex problems, rather than be bogged down in computation.

Define Algorithm

Algorithm a set of predefined steps applicable to a class of problems that gives the correct result in every case when the steps are carried out correctly

“Fluency without Fear: Research Evidence on the Best Ways to Learn Math Facts” Jo Boaler Cathy Williams Amanda Ciobfer

“Do We Really Want to Keep the Traditional Algorithms for Whole Numbers? John A. Van de Walle

Jigsaw the Articles Create teams of 5 Each team member is assigned a specific section to read Share information with team members Reach a conclusion based on all information shared

 Teaching for Memorization: refers to committing the results of unrelated operations to memory so that thinking is unnecessary  Teaching for Automaticity: refers to answering facts automatically, in only a few seconds without counting, but thinking about the relationships within facts is critical Fosnot & Dolk, Constructing Number Sense, Addition, and Subtraction, pg. 98

Computational Fluency……..defined Students have:  Efficient and accurate methods for computing  Flexibility in problem solving strategies  Conceptual understanding to explain strategies  Efficient production of accurate answers

Strategies  mathematical ideas that students understand well (i.e. base-ten number system, properties of multiplication and division, number relationships)  purposeful manipulations that may be chosen for specific problems, may be used to convert one problem into another strategies emphasizes student sense making

Strategies vs Algorithms When students compute with strategies they invent or choose because they are meaningful, their learning tends to be robust—they are able to remember and apply their knowledge.

Mindful Practice We know quite a bit about helping students develop fact mastery, and it has little to do with quantity of drill or drill techniques. If appropriate development is undertaken in the primary grades, there is no reason that all children cannot master their facts by the end of grade 3. Van de Walle & Lovin, Teaching Student-Centered Mathematics Grades K-3, pg. 94

Mindful Practice Practice should be purposeful and should focus on developing thinking strategies and a knowledge of number relationships rather than drill isolated facts. NCTM, Principles and Standards for School Mathematics, pg. 87

Supporting links on PROE site Mindful Practice  Games  Puzzles  Apps

Mathematical Practice Standards

Balanced Assessment

Assessment in the Implementation Guide

Assessment……………………defined Assessment is the process of collecting and interpreting information that informs educators, students, and families about students’ progress in attaining the knowledge, skills, attitudes, and behaviors to be learned or acquired in school (JCSEE, 2013).

Balanced Assessment System A balanced assessment system is the strategic use of formative, interim, and summative measures of student performance to address immediate student needs, inform ongoing instructional changes, and guide long-term educational improvement.

Formative Assessment……………defined designed to provide regular feedback to teachers so they can adjust instruction to improve student learning (Wiliam, 2011; Perie, Marion, & Gong 2009; Popham, 2009)

Interim Assessment……………defined designed to identify strengths and weaknesses in curriculum and instruction (Wiliam, 2011; Perie, Marion, & Gong 2009; Popham, 2009)

Summative Assessment……………defined designed to measure overall curriculum and program effectiveness; standardized to allow comparison across student groups (Wiliam, 2011; Perie, Marion, & Gong 2009; Popham, 2009)

Balanced Assessment System Summative Interim Formative Frequency of Administration Measuring Student Growth: A Collaborative Process End of Course/Year Assessments Performance-Based Assessments Portfolios Mid-Year Assessments Unit/Chapter Assessments Performance-Based Assessments Self/Peer Assessments Discussion/Observation/Checklists Adapted from Perie, Marion, & Gong (2009) 25 Achievement Instruction/Learning Progress

Turn & Talk Define the 3 parts of a Balanced Assessment System.

Focus: Assessment in the Classroom Formative

Brainstorm & List How do I currently utilize formative assessment practices and strategies?

Quick Look What information will I get from my students? How could I modify my instruction?

My Favorite No  What information will I get from my students? How could I modify my instruction?

Number Talk What information will I get from my students? How could I modify my instruction?

Compare = a) 24 b) 23 c) 22 d) Compute Show your work. 3. John Jill (add 1 extra) (add the extra 1 back) Who is correct and why? Explain any mistakes that were made. What information will I get from my students? How could I modify my instruction?

Formative Assessment the ongoing monitoring of student learning to inform instruction generally considered a hallmark of effective instruction in any discipline

What can/should we assess? Content KnowledgeMathematical DispositionWork Habits

Research indicates that student learning significantly improves when:  Teachers use assessment to inform their instruction  Students are provided frequent feedback on their progress

Formative Assessment = Teaching

Formative Assessment AnticipateAnalyzeAdapt

Anticipate  How students will engage with the problem  What strategies they might use  What content/topics will be challenging  What scaffolding will be needed  What evidence will show student understanding questionobservelistenadjust

Guiding Questions for Anticipation  What do my students know?  What are they able to do?  What is the evidence?  How does this shape what I do:  In the moment  In my plans for tomorrow

Analyze  Listens carefully  Takes role as an observer  Watches students’ interactions with each other  Watches students’ interactions with the math  Find out what students are thinking questionobservelistenadjust

Guiding Questions for Analysis  Are math tasks promoting learner independence?  Learner curiosity?  Mathematical thinking?  Confidence?  Disposition to do mathematics?

Adapt  Provide more time  Assist struggling students  Make connections with prior knowledge  Ask more challenging questions questionobservelistenadjust

Guiding Questions for Adaptation  How do I help students engage in solving problems?  How are the tasks effective in helping students learn math?  How do the problems stimulate students discussion?

Things to Consider when writing an assessment  Determine how you will use the data.  Target a set of grade-level standards  Consider Practice Standards too  Decide how you will elicit direct, observable evidence  Create a plan for feedback  Misconceptions and errors

Resources  Illustrative Mathematics  Inside Mathematics  Mars Tasks  Achieve the Core  EngageNY  Model Math Curriculum  IL Teach and Talk  IL Classrooms In Action – Balanced Assessment

K – Illustrative Mathematics

Grade 2 - LiveBinder

Grade 3 – Achieve the Core

Grade 5 – IL Teach & Talk

Grade 6 – Model Math Resources

Grade 8 - EngageNY

High School – Math Vision Project

Your Turn to Give it a Try Using everything you have just learned, create a formative assessment.  Think about what you are about to teach.  Use/modify/write a question or task  Choose a strategy  Discuss how you will use data to inform instruction.  Decide the type of feedback you will provide.

Feedback Provide feedback to another group on their assessment process.

Share Your Plan 57 With your loudest teacher voice, present the poster of your Research Lesson with the rest of the Cadre.