modifying elementary mathematics textbook lessons to implement

Modifying

elementary

mathematics

textbook lessons

to implement

Common Core

State Standards

Dr. Chepina Rumsey, Kansas State University

KDP Webinar - Nov. 11, 2013

Outline of Presentation

CCSS Background

Content, SMPs, Progression Documents

Shifts in Instruction

Example of an Inquiry-Based lesson protocol

Guiding Questions for Modifying Lessons

Part 1 – What

Part 2 – How

Modifying your own lessons

Questions

What do you know about the

CCSS?

How are they different than many other standards? More focused, coherent, rigorous

Attention on Understanding

Content and Practice Standards

Progression Documents

Hunt Institute video intro

by Bill McCallum:

http://www.youtube.com/watch?v=dnjbwJdcPjE&feature=c4-overview-vl&list=PL913348FFD75155C6

CCSS, 2010, p. 5

Where did the Standards for

Mathematical Practice come from?

(NCTM) National Council of Teachers of

Mathematics – Process Standards

Adding it Up –Strands of Mathematical

Proficiency

What are the Standards for Mathematical

Practice?

How do these focus our teaching goals

and how we expect students to be

engaged?

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.

2. Reason abstractly and quantitatively.

3. Construct viable arguments and critique the reasoning of others.

4. Model with mathematics.

5. Use appropriate tools strategically.

6. Attend to precision.

7. Look for and make use of structure.

8. Look for and express regularity in repeated reasoning.

Full descriptions for all SMPs are found at http://www.corestandards.org

SMP1 - Make sense of problems

and persevere in solving them.

Students can

start by explaining to themselves the meaning of a problem and looking for entry points to its solution. They analyze givens, constraints, relationships, and goals.

try analogous problems, and try special cases and simpler forms of the original problem in order to gain insight into its solution. They monitor and evaluate their progress and change course if necessary.

SMP 2 - Reason abstractly and

quantitatively.

Students can

make sense of quantities and their

relationships in problem situations.

decontextualize

contextualize

SMP 3 - Construct viable arguments

and critique the reasoning of others.

“One hallmark of mathematical

understanding is the ability to justify, in a

way appropriate to the student’s

mathematical maturity, why a particular

mathematical statement is true or where

a mathematical rule comes from.” (CCSS,

2010, p. 4)

Students can

understand and use stated assumptions, definitions, and previously established results in constructing arguments.

make conjectures and build a logical progression of statements to explore the truth of their conjectures.

analyze situations by breaking them into cases, and can recognize and use counterexamples.

justify their conclusions, communicate them to others, and respond to the arguments of others.

compare the effectiveness of two plausible arguments .

SMP 4 – Model with Mathematics

Students can

apply the mathematics they know to

solve problems arising in everyday life,

society, and the workplace.

make assumptions and approximations to

simplify a complicated situation.

interpret their mathematical results in the

context of the situation and reflect on

whether the results make sense.

SMP 5 – Use appropriate tools

strategically

Students can

consider the available tools when solving a mathematical problem.

make sound decisions about when each of these tools might be helpful (ex. pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet)

use technological tools to explore and deepen their understanding of concepts

SMP 6 – Attend to Precision

Students can

communicate precisely to others.

use clear definitions in discussion with

others and in their own reasoning.

state the meaning of the symbols they

choose, including using the equal sign

consistently and appropriately.

specify units of measure.

SMP 7 – Look for and make

sure of structure

Students can

look closely to discern a pattern or find

general structure in specific cases. (ex.

Commutative property of addition

7+3=3+7)

SMP 8 – Look for an express

regularity in repeated reasoning

Students can

notice if calculations are repeated, and

look both for general methods and for

shortcuts.

generalize from specific cases.

Designers of curricula, assessments, and

professional development should all

attend to the need to connect the

mathematical practices to mathematical

content in mathematics instruction.

(CCSS, 2010, p. 8)

ESSENTIAL QUESTIONS:

If these are the practices that students need

to be engaged in, what do we need to do

as teachers to encourage those practices? – How do we shift our teaching practices?

How can we modify our textbooks so that opportunities to encourage the practices is

presented to the students?

7 Shifts in Instruction

Bay$Williams,+J.+M.,+McGatha,+M.,+Kobett,+B.,+&+Wray,+J.+(in+press).+Mathematics*Coaching*Toolkit.+New+York,+NY:+Pearson.++

Shifts'in'Classroom'Practice'

Shift'1:'From!same!instruction!toward!differentiated!instruction.''

++'Shift'2:'From!students!working!individually!toward!community!of!learners.!!''

+

+

Shift'3:'From!mathematical!authority!coming!from!the!teacher!or!textbook!toward!mathematical!authority!coming!from!sound!student!reasoning.!

+

'

'Shift'4:'From!teacher!demonstrating!‘how!to’!toward!teacher!communicating!‘expectations’!for!learning.!'+

+

+

Shift'5:'From!content!taught!in!isolation!toward!content!connected!to!prior!knowledge.!++

+'Shift'6:'From!focus!on!correct!answer!toward!focus!on!explanation!and!understanding.'+

+

Shift'7:'From!mathematics<made<easy!for!students!toward!engaging!students!in!productive!struggle.'+

Differentiated+instruction+but+same+learning+outcomes+for+all+students.++

Same+instruction+for+all+students.++

Community+of+learners+where+students+hear,+share,+and+judge+reasonableness+of+strategies+and+solutions.++

Students+work+individually+on+tasks+and+seek+feedback+from+teacher+on+reasonableness+of+strategies+and+solutions.+

Correctness+of+solution+is+based+on+reasoning+about+the+accuracy+of+the+solution+strategy.+

Correctness+of+solutions+is+determined+by+seeking+input+from+teacher+or+textbook.+

Teacher+facilitates+high$level+performance+by+sharing+learning+goals+and+expectations+for+products+that+demonstrate+learning.+

Teacher+demonstrates+the+way+in+which+to+solve+a+problem+and+helps+students+in+solving+the+problem+in+that+way.+

Discussions+and+classroom+routines+focus+on+student+explanations+that+address+why+an+answer+is+(or+isn’t)+correct.+

Discussions+and+classroom+routines+focus+on+student+explanation+of+how+they+solved+a+task+and+if+it+is+correct.+

Content+presented+in+ways+where+explicit+attention+is+given+to+making+connections+among+mathematical+ideas.+

Content+presented+independent+of+its+connections+to+what+has+been+previously+learned.+

Teacher+poses+tasks+and+challenges+students+to+persevere+and+attempt+multiple+approaches+to+solving+problems.++

Mathematics+is+presented+in+small+chunks+and+help+is+provided+so+that+students+reach+solutions+quickly+and+without+higher+level+thinking.+





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Toward Inquiry-based Teaching

5E Model of Lesson Planning

Engage

Explore

Explain

Elaborate

Evaluate

Engage

In the engage section, teachers:

• Introduce lesson topic and provide focus

for the lesson

• Pique curiosity and engage thinking

• Probe conceptions and misconceptions

• Help students make connections with

prior knowledge

• Invite students to learn

Explore

• Provide hands-on opportunities for

exploration and discovery. Students

investigate a math concept and begin to

make generalizations. Students share their

thinking and ask questions.

• Teachers observe and listen, ask probing

questions to redirect, and provide

sufficient time. The teacher scaffolds

assistance.

Explain

Teachers help students make sense of

their observations and make connections.

Teachers use students questions, thinking

and observations to direct the focus to

the intended lesson. The teacher might

formally introduce vocabulary.

Elaborate

Teachers provide further activity allowing

the students to put new knowledge into

practice

Evaluate

Teachers assess student understanding

and lesson effectiveness

Modifying Textbooks –

Part 1 What

What is the content focus?

What are the objectives and goals?

What conceptual understanding do we want

students to gain?

What procedures is the textbook

focusing on?

What SMP focus lends itself well

to these concepts? Why?

Modifying Textbooks –

Part 2 How

How can we embed this SMP into the lesson?

How can we focus on conceptual understanding?

How can we give “mathematical authority” to

students?

How can we develop a community of learners?

How can we engage them in a productive

struggle?

How can we connect to other knowledge?

How can we focus on mathematical explanations?

Example 1

• What is the

content focus?

• What are the

objectives and goals?

• What conceptual

understanding do

we want students

to gain?

• What procedures

is the textbook focusing on?

• What SMP focus

lends itself well to

these concepts? Why?

Part 1: WHAT

• How can we embed

this SMP into the lesson?

• How can we focus on

conceptual

understanding?

• How can we give

“mathematical

authority” to students?

• How can we develop a

community of learners?

• How can we engage

them in a productive

struggle?

• How can we connect

to other knowledge?


mathematical

explanations?

Part 2: HOW

Example 2

• What is the

content focus?

• What are the

objectives and goals?

• What conceptual

understanding do

we want students

to gain?

• What procedures

is the textbook focusing on?

• What SMP focus

lends itself well to

these concepts? Why?

Part 1: WHAT

• How can we embed

this SMP into the lesson?


conceptual

understanding?

• How can we give

“mathematical

authority” to students?

• How can we develop a

community of learners?

• How can we engage

them in a productive

struggle?

• How can we connect

to other knowledge?


mathematical

explanations?

Part 2: HOW

Ideas: Encourage multiple solution strategies.

Allow students to explain strategies and tools.

Let students make connections between

strategies.

Let students look for patterns and make claims,

justify, and critique.

Ask the students if the properties are true for all

numbers, allow them to justify.

Have fewer practice problems, but require

explanation.

Look at your own textbooks

First think about the part 1 questions: What

is this about?

Then think about the part 2 questions:

How can I modify the lesson?

Final thoughts and questions…

Thank you!

[email protected]