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Mathematics
Leadership for the Mathematics Classroom
TEPSA Tour: 11.04.13
Janet Dodd, District Instructional SpecialistElementary Mathematics, Pasadena ISD
jdodd@pasadenaisd.org
Dr. Karen Hickman, Deputy SuperintendentAcademic Achievement, Pasadena ISD
khickman@pasadenaisd.org
Mathematics
Leadership for the Mathematics Classroom
• Welcome!• Goals:
• Explore what mathematics instruction should “look like” and “sound like”
• Explore strategies for creating collaborative teams of mathematics teachers
My Reflections & Next Steps: NCTM Administrator’s Guide (2003, pg. 9)
What is the teacher doing? Choosing “good” problems – ones that
invite exploration of an important mathematical concept and allow students the change to solidify and extend their knowledge
Using questioning techniques to facilitate learning
Encouraging students to explore multiple solutions
Creating a variety of opportunities, such as group work and class discussions, for students to communicate mathematically
Modeling appropriate mathematical language and a disposition for solving challenging mathematics problems
NCTM Administrator’s Guide (2003, pg. 9)
What are students doing? Actively engaging in the learning
process Reasoning and making conjectures
about the problem Communicating their mathematical
thinking orally and in writing Listening to and reacting to others’
thinking and solutions to problems Using a variety of representations,
such as pictures, tables, graphs, and words, for their mathematical thinking
Using mathematical and technological tools such as physical materials, calculators, and computers, along with textbooks and other instructional materials
My Reflections & Next Steps:
My Reflections & Next Steps:
“Assessment and instruction are often conceived as curiously separate in both time and purpose. The key to high-quality formative assessment is to intertwine the two. What teachers and students need is assessment and instruction that are conceived as a unit, employed as a unit, and applied as a unit.”
Graue (1993, pg. 4) in Greenstein (2010, pg. 24)
Preparing: Know the TEKS and the Scope &
Sequence Attending (district) Focus PDs Planning: Nine-Week Planning Day
o Mapping out the nine-weeks o Mapping out the bundles
Weekly Team Planning o Implementing the Data Cycle o Determining instructional adjustments
Monitoring: Monitoring lesson plans Observations/Walk-throughs Examining student work Analyzing student data
My Reflections & Next Steps:
Leadership for the Mathematics
Classroom 11.04.13
TEPSA Tour 11.04.13: Leadership for the Mathematics Classroom: Dr. Karen Hickman khickman@pasadenaisd.org & Janet Dodd jdodd@pasadenaisd.org Region 4 ESC materials used with permission from Region 4 ESC.
A&D Statements
Instruction
1. is smaller than .
Agree Disagree It Depends Not Sure My thinking:
Curriculum
2. Numerators must be smaller than denominators.
Agree Disagree It Depends Not Sure My thinking:
Making It Happen
3. Fractions can be written as decimals.
Agree Disagree It Depends Not Sure My thinking:
Assessment
Adapted from Mathematics Formative Assessment (Keeley & Tobey, 2011)
Mathematics
Leadership for the Mathematics Classroom
• Supporting Curriculum and Instruction– What would you see? What would you hear?
• Modeling addition and subtraction story problems
Sean had some crayons in his school supply box. He gave 6 crayons to Mayra. Now he has 8 crayons left. How many crayons did Sean have to begin with?
© 2007, Region 4 Education Service Center All Rights Reserved. Reproduction authorized only for the students of the teacher that attended this professional development.
Types of Addition and Subtraction Problem Situations
Type of Problem Situation
Join
Result Unknown Sean had 6 crayons. Mayra gave him 8 more crayons. How many crayons does Sean have in all?
Change Unknown Sean has 6 crayons. His teacher gave him some more crayons. Now Sean has 14 crayons. How many crayons did Sean’s teacher give him?
Start Unknown Sean had some crayons. Mayra gave him 6 more crayons. Now Sean has 14 crayons. How many crayons did Sean have to begin with?
Separate
Result Unknown Sean had 14 crayons in his school supply box. He gave 8 crayons to Mayra. How many crayons does Sean have left?
Change Unknown Sean had 14 crayons. He gave some of his crayons to Mayra. Now he has 6 crayons left. How many crayons did Sean give to Mayra?
Start Unknown Sean had some crayons in his school supply box. He gave 6 crayons to Mayra. Now he has 8 crayons left. How many crayons did Sean have to begin with?
Part/Part/Whole
Whole Unknown Sean has 8 red crayons and 6 blue crayons. How many crayons does he have?
Part Unknown Sean has 14 crayons in his school supply box. 6 crayons are red and the rest are blue. How many blue crayons does Sean have?
Compare
Difference Unknown Sean has 14 crayons in his school supply box. Mayra has 6 crayons in her school supply box. How many more crayons does Sean have than Mayra?
Larger Unknown Mayra has 8 crayons. Sean has 6 more crayons than Mayra. How many crayons does Sean have?
Smaller Unknown Sean has 14 crayons in his school supply box. He has 6 more crayons than Mayra. How many crayons does Mayra have?
Mathematics
Leadership for the Mathematics Classroom
• Supporting Curriculum and Instruction– What would you see? What would you hear?
• Engaging Mathematics: Grade 4 “Strategy Match”
Student Name: ________________________________ Date: ________________
Engaging Mathematics © Region 4 Education Service Center Grade 4 200 All rights reserved.
Strategy Match Activity Page • Cut apart the cards on the Strategy Match Activity Master. • Match each multiplication fact with a strategy that could be used to find the fact’s
product. • Glue or tape the cards in My Workspace. My Workspace
Communicating about Mathematics Choose a set of matched cards. What is another strategy that could be used to determine the product?
Student Name: ________________________________ Date: ________________
© Region 4 Education Service Center Engaging Mathematics All rights reserved. 201 Grade 4
Strategy Match Activity Master
7 3× 8 6× 9 4×
6 3× 7 5× 10 2×
4 4× 3 9×
6,12,18
9+9+9
Mathematics
Leadership for the Mathematics Classroom
• Supporting Curriculum and Instruction– What would you see? What would you hear?
• Math Talks
http://mathsolutions.wistia.com/medias/k46tk935kw
Mathematics
Leadership for the Mathematics Classroom
• Supporting Curriculum and Instruction– What would you see? What would you hear?
• What does NCTM say?(National Council of Teachers of Mathematics
– Reflections & Next Steps
Mathematics
Leadership for the Mathematics Classroom
• Supporting Assessment– What would you see? What would you hear?
• A&D Statements• Student Work Samples
– Comments-Only Marking• Concept Attainment Cards
Mathematics
“Assessment and instruction are often conceived as curiously separate in both time and purpose. The key to high-quality formative assessment is to intertwine the two. What teachers and students need is assessment and instruction that are conceived as a unit, employed as a unit, and applied as a unit.”
Graue (1993, pg. 4) in Greenstein (2010, pg. 24)
Leadership for the Mathematics Classroom
Mathematics
Leadership for the Mathematics Classroom
• Supporting Assessment– What would you see? What would you hear?– Reflections & Next Steps
PLC Data Cycle
Facilitate Instruction and
Monitor with Formative
Assessments
Administer Common
Assessments Across Teams
Analyze Data from Common Assessments and Plan for Re-teaching
and Enrichment
Develop Assessments for Targeted
SEs and Collaborate to
Plan Instruction
Beginning of a Unit End of a Unit
Mathematics
Leadership for the Mathematics Classroom
• Administrative Support – How do you create an effective structure for
collaborative planning?• Preparing
• Know the TEKS• Know the Scope & Sequence• Attend Focus (district) PDs• Utilize Standard Clarification documents
Pasadena ISD 3rd Grade Mathematics Standard Clarification: 3.4B (Readiness Standard)
© Pasadena ISD All rights reserved. Reproduction authorized only for the teachers of Pasadena ISD. 1
Mathematics TEKS
3.4 Number, Operation, and Quantitative Reasoning (Reporting Category 1) The student recognizes and solves problems in multiplication and division situations. 3.4B Solve and record multiplication problems (up to two digits times one digit).
(Readiness Standard)
Process Standards
The Process Standards should be incorporated into instruction on a daily basis. The student applies Grade 3 mathematics to solve problems connected to everyday
experiences and activities in and outside of school. (TEKS 3.14A, 3.14B, 3.14C, 3.14D) The student communicates about Grade 3 mathematics using informal language.
(TEKS 3.15A, 3.15B) The student uses logical reasoning. (TEKS 3.16A, 3.16B)
ELPS & Language Objective
Possible ELPS: Speaking (c)3(D) Share information in cooperative learning interactions; Possible Language Objective: TSW share information about how she/he solved multiplication problems in an “inside
outside circle”.
Prior Knowledge
2.4A Model, create, and describe multiplication situations in which equivalent sets of concrete objects are joined.
Possible Core
Vocabulary array, factor, product, partial product, area model, equal groups matriz, factor, producto, productos parciales, modelo del área, grupos iguales
Instructional Clarifications Select and use multiplication to determine the solution to a problem.
o Utilize a problem-solving model/guide such as the "UPS Check/Reflect" tool or “RAPS”. o Utilize a variety of contexts that might include tables, pictures, and/or other graphic
organizers. o Problems could be single or multistep, could incorporate multiple operations, could have
extra information, could incorporate the word “not”, and could have “not here” listed as an answer choice (if multiple choice format).
o Problems could embed concepts from within the same Reporting Category or from other Reporting Categories.
o Estimate solutions before computing a solution. o Represent multiple solution strategies (including flexible strategies) with words and
number sentences. o Explain a solution process and justify the reasonableness of the solution.
TEKS Clarifications
Multiplication
Solve and record multiplication problems. Example: There are 8 spiders in a jar. If each spider has 8 legs, how many spider legs are there all together? Possible Solution Strategies: Draw a picture, use concrete models, use repeated addition, or use multiplication.
Answer: The product is 64. 8+8+8+8+8+8+8+8=64 or 8 8 = 64.
Pasadena ISD 3rd Grade Mathematics Standard Clarification: 3.4B (Readiness Standard)
© Pasadena ISD All rights reserved. Reproduction authorized only for the teachers of Pasadena ISD. 2
Example: James loads boxes on trucks for a shipping company. On Tuesday, James loaded 5 trucks with 52 boxes in each truck. How many boxes did James load on trucks on Tuesday? Possible Solution Strategy: Use base ten blocks in an area model.
Using partial products:
52 5 10 52 = 10 + 250 550 = 250 260
Answer: The product is 260. 52 5 = 260.
Solve multiplication problems. Example: Jacquelyn’s choir had 95 members. Each member sang 3 solos for individual competitions during last month’s regional performance. How many solos did Jacquelyn’s choir sing all together? Understanding the Problem:
Ask the students, “What are you trying to find out?” Ask the students to restate the problem.
Possible Answer: “We need to find out how many total solos were sung by the 95 choir members.” Making a Plan:
Ask the students, “Are you joining equal sets or separating sets of objects into equal groups?” Ask the students, “What is the important information in the problem?”
Possible Answer: “We are joining equal sets, so we will multiply. The important information in the question is the number of choir members and the number of solos.” Carrying out the Plan:
Ask the students, “How did you solve the problem?” Possible Answer: “We multiplied 95 by 3.” Evaluating for Reasonableness:
Ask the students, “How do you know your answer is reasonable?” Possible Answer: “We knew that each choir member sang 3 solos, and there were 95 choir members. We estimated 95 as 100. So, 100 ×3 = 300 and 300 is close to 285. We multiplied 95 by 3 to get our answer.” Answer: 285 solos Additional components of Standard Clarification documents: resources for instruction, assessment, technology connections, intervention, and enrichment.
4th Grade Writing
Sample provided by Pasadena ISD. Adapted from lead4ward standard clarification tools.
4.15A Readiness (4.15) Writing/Writing Process. Students use elements of the writing process (planning, drafting, revising, editing, and publishing) to compose text. Students are expected to (A) plan a first draft selecting a genre appropriate for conveying the intended meaning to an audience and generating ideas through a range of strategies (e.g., brainstorming, graphic organizers, logs, journals)
Content Builder Rigor ImplicationsWhat do students need to know? Content
Connections
To what degree will this learning impact learning two years down the road?
Create Evaluate Analyze Apply
Understand Remember
Verb
Level of Bloom’s Taxonomy
Instructional Implications:
Academic Vocabulary
Distractor Factor
Mathematics
Leadership for the Mathematics Classroom
• Administrative Support – How do you create an effective structure for
collaborative planning?• Planning
• Nine-Week Planning Day• Map out the nine-weeks• Map out instructional bundles
• Weekly Team Planning• Implement the data cycle• Determine instructional adjustments
Mathematics
Leadership for the Mathematics Classroom
• Administrative Support – How do you ensure the effectiveness of
collaborative planning?• Monitoring
• Monitor lesson plans• Observations/walk-throughs• Examine student work• Analyze student data
– Reflections & Next Steps
Mathematics
Leadership for the Mathematics Classroom
• Closure: – Individual Reflections:
• What is one of your “take-aways” from today’s discussions?
– Find a Partner, Share, & Sum It Up: • You may start with one of the following sentence starters:
– I hear you saying …– So, if I understand you correctly …– I like how you said …
Sum it Up Card
Rephrase what your partner said in a shorter version. You may start with one of the following sentence starters:
I hear you saying … So, if I understand you correctly … I like how you said …
Sum it Up Card
Rephrase what your partner said in a shorter version. You may start with one of the following sentence starters:
I hear you saying … So, if I understand you correctly … I like how you said …
Sum it Up Card
Rephrase what your partner said in a shorter version. You may start with one of the following sentence starters:
I hear you saying … So, if I understand you correctly … I like how you said …
Sum it Up Card
Rephrase what your partner said in a shorter version. You may start with one of the following sentence starters:
I hear you saying … So, if I understand you correctly … I like how you said …
Adapted from Total Participation Techniques (Himmele & Himmele, 2011)
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