math instructional leadership cadre session 3 november 16 th and 18 th
TRANSCRIPT
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.