Session 3 November 16 th and 18 th Math Session 3 Fluency vs Algorithms Mathematical Practices 7 amp 8 Balanced Assessment Define Fluency The Importance of Fact Fluency When students are ID: 640211
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Slide1
Math Instructional Leadership Cadre
Session 3
November 16
th
and 18
th
Slide2
Math Session 3
Fluency vs Algorithms
Mathematical Practices 7 & 8
Balanced AssessmentSlide3
Define FluencySlide4
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. Slide5
Define AlgorithmSlide6
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 correctlySlide7
“Fluency without Fear: Research Evidence on the Best Ways to Learn Math Facts”
Jo
Boaler
Cathy Williams
Amanda
CiobferSlide8
“Do We Really Want to Keep the Traditional Algorithms for Whole Numbers?
John A. Van de
WalleSlide9
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 sharedSlide10
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. 98Slide11
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 answersSlide12
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 makingSlide13
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
.Slide14
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. 94Slide15
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. 87Slide16
Supporting links on PROE site
Mindful Practice
Games
Puzzles
AppsSlide17
Mathematical Practice StandardsSlide18
Balanced AssessmentSlide19
Assessment in the Implementation GuideSlide20
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).Slide21
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. Slide22
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)Slide23
Interim Assessment……………defined
designed to identify strengths and weaknesses in curriculum and instruction
(
Wiliam
, 2011;
Perie
, Marion, & Gong 2009;
Popham
, 2009)Slide24
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)Slide25
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
ProgressSlide26
Turn & Talk
Define the 3 parts of a Balanced Assessment System.Slide27
Focus: Assessment in the Classroom
FormativeSlide28
Brainstorm & List
How
do I currently utilize formative assessment practices and strategies?Slide29Slide30
Quick Look
What information will I get from my students?
How could I modify my instruction?Slide31
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?Slide32
Number Talk
What information will I get from my students?
How could I modify my instruction?
https://www.youtube.com/watch?v=Ihz-0pGmhLI
Slide33
Compare
14 + 9 =
24
23
22
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?Slide34Slide35
Formative Assessment
the
ongoing monitoring of student learning to inform
instruction
generally
considered a hallmark of effective instruction in any
disciplineSlide36
What can/should we assess?Slide37
Research indicates that student learning significantly improves when:
Teachers
use assessment to inform their
instruction
Students are provided frequent feedback on their progressSlide38
Formative Assessment
=
TeachingSlide39Slide40
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 understandingSlide41
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 tomorrowSlide42
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 thinkingSlide43
Guiding Questions for Analysis
Are math tasks promoting learner independence?
Learner curiosity?
Mathematical thinking?
Confidence?
Disposition to do mathematics?Slide44
Adapt
Provide more time
Assist struggling students
Make connections with prior knowledge
Ask more challenging questionsSlide45
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?Slide46
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
errorsSlide47
Resources
Illustrative Mathematics
Inside Mathematics
Mars Tasks
Achieve the Core
EngageNY
Model Math Curriculum
IL Teach and Talk
IL Classrooms In Action – Balanced AssessmentSlide48
K – Illustrative MathematicsSlide49
Grade 2 - LiveBinderSlide50
Grade 3 – Achieve the CoreSlide51
Grade 5 – IL Teach & TalkSlide52
Grade 6 – Model Math ResourcesSlide53
Grade 8 - EngageNYSlide54
High School – Math Vision ProjectSlide55
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. Slide56
Feedback
Provide feedback to another group on their assessment process. Slide57
Share Your Plan
57
With your loudest teacher voice, present the poster of your Research Lesson with the rest of the Cadre.