Modifying elementary mathematics textbook lessons to implement
Transcript of Modifying elementary mathematics textbook lessons to implement
![Page 1: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/1.jpg)
Modifying
elementary
mathematics
textbook lessons
to implement
Common Core
State Standards
Dr. Chepina Rumsey, Kansas State University
KDP Webinar - Nov. 11, 2013
![Page 2: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/2.jpg)
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
![Page 3: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/3.jpg)
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
![Page 4: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/4.jpg)
CCSS, 2010, p. 5
![Page 5: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/5.jpg)
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?
![Page 6: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/6.jpg)
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
![Page 7: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/7.jpg)
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.
![Page 8: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/8.jpg)
SMP 2 - Reason abstractly and
quantitatively.
Students can
make sense of quantities and their
relationships in problem situations.
decontextualize
contextualize
![Page 9: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/9.jpg)
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)
![Page 10: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/10.jpg)
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 .
![Page 11: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/11.jpg)
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.
![Page 12: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/12.jpg)
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
![Page 13: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/13.jpg)
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.
![Page 14: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/14.jpg)
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)
![Page 15: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/15.jpg)
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.
![Page 16: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/16.jpg)
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)
![Page 17: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/17.jpg)
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?
![Page 18: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/18.jpg)
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.+
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.+
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.+
![Page 19: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/19.jpg)
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.+
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.+
![Page 20: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/20.jpg)
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.+
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.+
![Page 21: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/21.jpg)
Toward Inquiry-based Teaching
5E Model of Lesson Planning
Engage
Explore
Explain
Elaborate
Evaluate
![Page 22: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/22.jpg)
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
![Page 23: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/23.jpg)
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.
![Page 24: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/24.jpg)
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.
![Page 25: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/25.jpg)
Elaborate
Teachers provide further activity allowing
the students to put new knowledge into
practice
![Page 26: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/26.jpg)
Evaluate
Teachers assess student understanding
and lesson effectiveness
![Page 27: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/27.jpg)
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?
![Page 28: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/28.jpg)
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?
![Page 29: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/29.jpg)
Example 1
![Page 30: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/30.jpg)
• 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
![Page 31: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/31.jpg)
• 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?
Part 2: HOW
![Page 32: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/32.jpg)
Example 2
![Page 33: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/33.jpg)
• 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
![Page 34: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/34.jpg)
• 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?
Part 2: HOW
![Page 35: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/35.jpg)
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.
![Page 36: Modifying elementary mathematics textbook lessons to implement](https://reader030.fdocuments.us/reader030/viewer/2022032806/623ec1b58b67de3aba0c8563/html5/thumbnails/36.jpg)
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?