Rigor Breakdown 2 Rigor Breakdown Part 1 Conceptual Understanding Grades 35 Session Objectives 4 Examine the conceptual understanding component of rigor in G3M5 Explore conceptual understanding for select content from grades ID: 782522
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Slide1
Rigor Breakdown
A Three Part Series
Slide2Rigor Breakdown
2
Slide3Rigor Breakdown
Part 1: Conceptual Understanding
Grades 3–5
Slide4Session Objectives
4
Examine the conceptual understanding component of rigor in
G3—M5
.
Explore conceptual understanding for select content from grades
4
and
5.
Explore how cross-grade coherence is accessible through conceptual understanding.
Recognize opportunities to emphasize the Standards of Mathematical Practice during activities that promote conceptual understanding.
Slide5Conceptual Understanding Revisited
5
“
Teachers teach more than ‘how to get the answer’ and instead support students’ ability to access concepts from a number of perspectives so that students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of core math concepts by applying them to new situations as well as writing and speaking about their understanding
.”
(excerpt from the Shifts)
Slide6Conceptual Understanding Revisited
6
Reflection:
What does conceptual understanding look like / sound like in the classroom?
Slide7Conceptual Understanding Revisited
7
Accessible through use of:
Concrete and pictorial models
R
eal-world contexts
Conceptual questioning
S
peaking and writing about understanding
Slide8AGENDA
8
Promoting Understanding through Models and Contexts
Questioning
, Writing and
Speaking about Understanding
Examine examples from G3—M5.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide9Lesson Engagement – The Number Line
9
Reflection:
What mathematical practice(s) do you see being enacted in the lesson?
Slide10G3—M5 Models and Contexts
10
Reflection:
What mathematical practice(s) do you see being enacted in the lesson?
Slide11AGENDA
11
Promoting Understanding through Models and Contexts
Questioning
, Writing and
Speaking about Understanding
Examine examples from G3—M5.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide12Lesson Engagement – Selecting Models and Contexts
12
Select a grade level: 4 or 5
Find a partner to work with.
Have your standards available.
Have your Number and Operations – Fractions progression available.
Have the
A Story of Units Curriculum Overview
available.
Slide13Lesson Engagement – Selecting Models and Contexts
13
Review this standard:
Grade 4: Grade 5:
4.NF.4 5.NF.3
Slide14Lesson Engagement – Selecting Models and Contexts
14
Decide on the model(s) – concrete and/or pictorial
Decide on contextual situations
Create a sample vignette to introduce the main concept
Slide15AGENDA
15
Promoting Understanding through Models and Contexts
Questioning
, Writing and
Speaking about Understanding
Examine examples from
G3—M5
.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide16Bridging Gaps in Prerequisite Knowledge
16
What prerequisite
understanding
is important for success in this lesson?
Slide17Bridging Gaps in Prerequisite Knowledge
17
How can my models and contexts be used / modified / supplemented to bridge the gaps?
Slide18Coherence Across the Grades
18
Reflections
What can you share with your colleagues to promote coherence relative to models and contexts across grades PK–5?
Recall that
A Story of Units
recommends a finite number of concrete and pictorial models used coherently across the grades.
Slide19AGENDA
19
Promoting Understanding through Models and Contexts
Questioning, Writing and Speaking about Understanding
Examine examples from G3—M5.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide20Video Clip – Conceptual Questioning
20
How do these questions prepare students for thinking about fractional units?
Which is a larger unit, an inch or a centimeter?
Therefore which would yield a greater number when measuring the book, inches or centimeters?
Slide21Video Clip: Inches and Centimeters
21
Slide22Video Clip – Conceptual Questioning
22
How do these questions prepare students for thinking about fractional units?
Which is a larger unit, an inch or a centimeter?
Therefore which would yield a greater number when measuring the book, inches or centimeters?
Slide23Conceptual Questioning – Key Points
23
Goes beyond getting the right answer
Goes beyond Yes/No questions
Encourages recognition of subtleties and exposes current level of student understanding
“Can you think of a case where that would
not
work?”
“Someone else says the answer is this. Can you prove that they are right/wrong?”
“When we get a like unit for these two fractions, will the like unit be bigger or smaller than the units we have?”
“Can you think of a number between 1/4 and 1/5?”
Slide24Lesson Engagement –
Examples of Conceptual Questioning
24
Find other examples of conceptual questioning
from the lessons in G3—M5.
Slide25AGENDA
25
Promoting Understanding through Models and Contexts
Questioning, Writing and Speaking about Understanding
Examine examples from G3—M5.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide26Lesson Engagement –
Selecting Conceptual Questions
26
Select conceptual questions to add to your lesson for Grade
4
or Grade
5
that assess and remediate gaps in prerequisite knowledge.
Slide27AGENDA
27
Promoting Understanding through Models and Contexts
Questioning, Writing and Speaking about Understanding
Examine examples from G3—M5.
Select strategies for Grades 4 and 5.
Consider ways to bridge gaps in prerequisite knowledge.
Slide28Conceptual Questioning
28
Reflection:
Think of a time when you were asked a question and were surprised to find out that you really did know the answer to that question – you just had to think about it.
Slide29Bridging Gaps in Prerequisite Knowledge
29
Design lesson opening questions geared to uncover current understanding of prerequisite knowledge.
Example – assess conceptual understanding of multiplication before learning to multiply with fractions:
Write a word problem that requires me to multiply 3 x 7 to get the answer.
Slide30Bridging Gaps in Prerequisite Knowledge
30
Work with your partner to design a conceptual question that assesses and bridges gaps in prerequisite knowledge for the lesson you’ve created.
Slide31Key Points
31
Conceptual understanding can be promoted in a variety of ways – concrete and pictorial models, real-world contexts, conceptual questioning, and writing/speaking about understanding.
Each of these ways can be used to coherently bridge gaps in prerequisite knowledge.
Content knowledge directed by the standards and the progressions informs coherent and balanced instruction.
Slide32Next Steps
32
How can you increase students’ deep understanding of the concepts you will be covering when you return to your schools?
How can you increase coherence in your school’s delivery of concepts?
What can you share with your colleagues about bridging gaps in prerequisite knowledge through conceptual models, contexts and questioning?