Math Instructional Leadership Cadre

Session 3November 16th and 18th

Math Session 3Fluency vs Algorithms

Mathematical Practices 7 & 8Balanced 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 BoalerCathy WilliamsAmanda 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……..definedStudents have:Efficient and accurate methods for computingFlexibility in problem solving strategiesConceptual understanding to explain strategiesEfficient 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 siteMindful 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 SystemA 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

• Performance-Based Assessments• Self/Peer Assessments• Discussion/Observation/Checklists

Adapted from Perie, Marion, & Gong (2009)25

Achievement

Instruction/Learning

Progress

Turn & TalkDefine the 3 parts of a Balanced Assessment System.

Focus: Assessment in the ClassroomFormative

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

https://www.youtube.com/watch?v=Rulmok_9HVs&t=36

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?

https://www.youtube.com/watch?v=Ihz-0pGmhLI

Compare1. 14 + 9 =

a) 24b) 23c) 22d) 21

2. Compute 14 + 9. Show your work.

3. John Jill 14 + 9 14 + 9 13 + 1 + 9 14 + 10 (add 1 extra) 13 + 10 24 23 25 (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 Knowledge

Mathematical Disposition

Work 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

Anticipate Analyze Adapt

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

question

observe

listen

adjust

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

question

observe

listen

adjust

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

question

observe

listen

adjust

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 TryUsing 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.

FeedbackProvide 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.