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New York State Academy for Teaching and LearningLearning Experience/Information Form

Please complete the following and return this form with the learning experience.

Personal Information:

Name: Connie Kudrna

Address: 102 Pullman Avenue Buffalo NY 14217

Home Phone: 716 874-4646 Home FAX: none available

E-mail: [email protected]

Current Teaching Position:Grade level(s) First Grade Subject(s): Math

School District Name: Buffalo Public Schools

School Name: Early Childhood Center 61

School Address: 546 Leroy Street Buffalo NY 14215

School Phone: 716 816-3400 School FAX: NA

E-mail: [email protected]

Title of Learning Experience: What’s the Problem?Standard area(s): Only list the standard area assessed through your learning experience assessment plan.

Math Science Technology 3 (MST 3)Math Standard 3

Circle the performance indicator level being assessed through this learning experience:

Elementary Beginning Level Intermediate Commencement

Alternate/Students with Disabilities

Peer Review Date(s): 11/3/05 Daemen class, 11/7/05 TAP meeting, 2/28/06 Daemen Class, 3/2/06 Daemen Class

SOS New York University Conference May 19, 2006 7/18/05 TAP meeting

Connie Kudrna 1 5/23/2023

Purpose: to assess students’ ability to apply basic math problem solving skills and strategies after completing a variety of practice activities.

Goals: Students will be able to understand the concepts of and become proficient with the skills of mathematics; communicate and reason mathematically; become problem solvers by using appropriate tools and strategies; through the integrated

study of number sense and operations and algebra.

Enduring Understanding: There is more than one way to solve a problem.

Essential Questions: When are some strategies better than others for solving mathematical problems? How are solutions to mathematical problems communicated? How can I solve mathematical problems? (student friendly)

Guiding questions: Which mathematical strategies can be used to solve the problem?

The objectives to be achieved are as follows:1. To use the following steps to solve problems:

1. interpret information in a word problem by underlining known information2. draw a picture of the known information to assist in identifying the problem3. identify the problem4. select and try possible strategies to solve the problem5. use pictures, words, and numbers to communicate the solution

2. To use some or all of the following mathematical strategies to solve and communicate solutions for a mathematical word problems:

act out story problems use physical objects to model the action in the problem use drawings, symbols, and pictures to model the action in the problem count by ones or grouping (tally marks) add and subtract using number sentences use trial and error use process of elimination work backwards use a t-chart make a graph use an algorithm

Grade Level and Ability: The students are instructed on a first grade level, however, many of the students are academically below level. There are 14 boys and one girl in a self contained class (15:1) and the breakdown of handicapping conditions is two MD (mentally disabled), three OHI (other health impaired) and ten LD (learning disabled).

Connie Kudrna 2 5/23/2023

LEARNING CONTEXT

Congruency TableLevel: Elementary Grade level: First

Title of Learning Experience: What’s the Problem?New York State Learning Standard: Math Science Technology (MST)Content Standard: Standard 3 Mathematics - Students will:

understand the concepts of and become proficient with the skills of mathematics; communicate and reason mathematically; become problem solvers by using appropriate tools and strategies; through the integrated study of number sense and operations, algebra,

geometry, measurement, and statistics and probability.

Process Strand: Problem Solving Strand Major Understanding: Students will build new mathematical knowledge through problem solving.

Performance Indicator

Instructional Task(Teacher friendly)

Instructional Task(Student Friendly)

Learning Objective Student Work Assessment

1.PS.2 Interpret information correctly, identify the problem, andgenerate possible solutions

Use modeling and guided practice to recognize known and unknown information in word problems

Use the plan and label strategy to correctly identify the problem

Select a strategy and solve the problem

Read the problem independently or with assistance from others

Use pencil to underline and circle story information with or without assistance

Experiment with solutions that would solve the problem

Circle the known information.

Underline the unknown information

Solve the problem

Crunchy Cookies

Missing Squares

Sweet Treats

Circus Cents

Building Blocks

Think-a-aloud

Self-made book Problem

Finding and Communicating Information dimension on What’s the Problem? Rubric

Teacher Observation Math Checklist

Major Understanding: Students will solve problems that arise in mathematics and in other contexts.Performance

IndicatorInstructional Task(Teacher friendly)



1.PS.3 Act out or model with manipulative activities involving mathematical content from literature and/or story telling

Use modeling and guided practice to act out mathematical ideas from stories with manipulatives

Create a play from the book Ten Black What’s the Problem?

Use What’s the Problem? to act out story and to find solution to word problems

Learn and practice Think-aloud

Act out the play with Think-aloud narration, choral and individual participation

Concrete Problem Solving Strategies dimension on What’s the Problem? Rubric


Major Understanding: Students will apply and adapt a variety of appropriate strategies to solve problems.1.PS.5 Use informal counting strategies to find solutions

Use modeling and guided practice to count and find solutions to mathematical problems

Use informal counting to show solutions to Missing Square story problem

Use Plan and Label problem solving strategy

Use informal counting to follow the problem solving steps

Missing Squares

Think-aloud

Abstract Problem Solving Strategies dimension onWhat’s the Problem? Rubric


1.PS.8 Use manipulatives (e.g., tiles, blocks) to model the action in problems

Use modeling and guided practice,use manipulatives to model solutions to a word problem

Use cubes to show solutions to Missing Squares story

Use Plan and Label problem solving strategy

Use cubes and to follow the problem solving steps

Missing Squares

Sweet Treats

Concrete Problem Solving Strategies dimension on What’s the Problem? Rubric

Teacher Observation Math

ChecklistPerformance

IndicatorInstructional Task(Teacher friendly)



1.PS.9 Use drawings/pictures to model the action in problems

As guided practice: Explain solutions to word problems to communicate mathematical thinking

Draw pictures to find answer to the questions

Use mathematical strategies and tools to communicate solutions for a mathematical problem

Missing Squares

Sweet Treats

Self-made books

Abstract Problem Solving Strategies dimension on What’s the Problem? Rubric


Process Strands: Representation StrandMajor Understanding: Students will select, apply, and translate among mathematical representations to solve problems.





1.R.4 Connect mathematical representations with problem solving

Communicate mathematical thinking by describing the steps and strategies used to solve a problem

Draw pictures, words, numbers to show answers

Represent word problems using pictures, words and numbers

Crunchy Crackers

Missing Squares

Sweet Treats

Circus Cents

Building Blocks

Think-a-aloud

Self-made book

Finding and Communicating Information dimension on What’s the Problem? Rubric


Content Strand: Number Sense and OperationsBand: Number SystemsMajor Understanding: Students will understand numbers, multiple ways of representing numbers, relationships among numbers, and number systems





1.N.10 Draw pictures or other informal symbols to represent a spoken number up to 20

Use symbols and numbers to represent addition and/or subtraction when solving problems

Use +, -, = or numbers to make number sentence

Write a number sentence using symbols (+, -, =)and numbers to solve the problem

Crunchy Crackers

Missing Squares

Sweet Treats

Circus Cents

Building Blocks

Self-made book

Abstract Problem Solving Strategies dimension on What’s the Problem? Rubric


Band: OperationsMajor Understanding: Students will understand meaning of operations and procedures and how they relate to one another1.N.24 Develop and use strategies to solve addition and subtraction word problems

Develop one or more strategies to solve word problems

Solve a word problem using strategies:Plan and labelThink aloudAct outDrawSymbolsCountAdd and subtractTrial and errorProcess of elimination

Use a number sentence, words,Pictures and/or manipulatives to find solutions for a word problem

Crunchy Crackers

Missing Squares

Sweet Treats

Circus Cents

Building Blocks

Think-a-aloud

Abstract Problem Solving Strategies dimension onWhat’s the Problem? Rubric


Physical objectAlgorithm

Self-made book

What students need to know and be able to do to succeed:

Prior to the Learning Experience:The Buffalo School District uses the Investigations in Numbers, Data and Space math program, developed by TERC and published by Scott Foresman. At the beginning of this math program, it is important to develop procedures and rules for all of the activities, such as for journaling and for small and whole group work.

Students have also practiced:CLASSROOM MANAGEMENT

Classroom rules: We immediately follow adult directions. We keep our hands and feet to ourselves. We work safely and share classroom resources.

We take turns talking. Classroom procedures:

Large Group Procedures: Sit cross leg, in a horseshoe on rug. Students raise hands to respond to questions. Students listen quietly as others speak.

Small Group Procedures: Secure the materials that you need to complete the activity.

Students are given the opportunity to select the level of difficulty of the task. Work quietly in your group. Everyone will contribute. Share your answers in large group.

Material Management: In small groups the students decide among themselves who retrieves and distributes the materials.

The same person is responsible for returning the materials to the proper place. Everyone in the group is responsible for clean-up of their personal space.

Presentation Procedures:Teacher draws a craft stick (popsicle stick) with a student’s names to determine who presents. Student presenter sits in the author chair next to the teacher in the front of the room.Other students are seated in a circle on the floor and follow large group procedures.

CONTENT KNOWLEDGE AND SKILLS communicate

orally act out story problems

use physical objects to model the action in the problem use drawings, symbols, and pictures to model the action in the problem count by ones or grouping (tally marks) count objects (Note: students should have the prerequisite skill to count objects with

one-to-one correspondence to number. If skill is absent, the task will need to be differentiated with this skill being the summative goal for that student.)

ASSESSMENT PLAN

The assessment plan includes both teacher and student use of a rubric. Following each task students use the student friendly rubric to self-assess. The teacher uses the Scoring rubric and tracks student progress on a Scorecard. The teacher comments on student work detailing what each student can do and what each struggles with.

While students are working the teacher observes and records their level of independence in employing math skills.

A similar problem is used for pre and post assessments to document achievement of the learning standards.

When solving the problems students circle the unknown, solve the problem and then circle the answer. This provides a visual connection between the problem and the solution.

The following tools are used to assess and document student progress:

What’s the Problem? Rubric to score how well students locate information and use concrete and abstract problem solving strategies (teacher-friendly, and student-friendly versions) using math journals

Teacher observation and anecdotal recording on Teacher Observation Math Checklist for classroom math instruction

Scorecard for What’s the Problem? Learning Experience for documenting teacher and student scoring of work samples.

Student: What’s the Problem? Scoring Rubric (teacher) Score:DIMENSIONS DISTINQUISHED 3 PROFICIENT 2 DEVELOPING 1

FINDING AND COMMUNICATING INFORMATION

The extent to which student: Solves the problem and find

answers (1.PS.2) Shows work of how to solve the

problem (1.N.2) Communicates the answers

(1.R.4)

Task: Journals Five Black Squares Book

Underlines what is known without help from others

Circles what is not known without help from others

Communicates answers by speaking and writing in journal without help from others

Underlines what is known with 1 or 2 prompts from others

Circles what is not known with 1 or 2 prompts from others

Communicates answers by speaking and writing in journal with 1 or 2 prompts from others

Can find known and unknown information only if teacher provides one-on-one instruction

Communicating answers requires one-on-one instruction

CONCRETE PROBLEM SOLVING STRATEGIES

The extent to which student: Participates in acting out

the story (1.PS.3) Uses manipulatives to find

answer (1.PS.8)

Task: Acting out story Journals Five Black Squares Book

Acts out the story without prompts from others

OR

Uses manipulatives to find answers without help from teacher or others

Acts out the story with 1 or 2 prompts from others

OR

Uses manipulatives to find answers with 1 or 2 assists from teacher

Acts out the story with 3 or more prompts from others

OR

Uses manipulatives to find answers only if teacher provides one-on-one instruction

ABSTRACT PROBLEM SOLVING STRATEGIES

The extent to which student: Counts to find answer (1.PS.5) Draws accurate pictures to find

answer (1.PS.9) Draws pictures or signs to show

answers (1.N.10)

Task: Journals Five Black Squares Book

Can count and answer questions without manipulatives.

Drawings contain no mistakes and were reached without using manipulatives and without help from others

Can count with the use of manipulatives

Drawings contain 1 or 2 mistakes and were reached with assistance from manipulatives and/or others

Must use manipulatives and count to find the answer with one-on-one instruction

Unable to solve the problem using an abstract problem solving strategy

COMMENTS:

Student name: Student Rubric What’s the Problem? Score:

DIMENSION DISTINQUISHED3

PROFICIENT2

DEVELOPING1

FINDING WHAT I NEED

Underline

Circle

I can do this by myself. I need help.

I can’t do this.

DOING

Act out story

Use counters I can do this by myself.I need help.

I can’t do this.

THINKING

Drawing pictures

Counting

Adding and subtracting

COMMENTS:

I can do this by myself.

I need help. I can’t do this.


Date: Assignment:

StudentName

Classroom Management,

Prompting

Not needed = N# = times needing prompting

LocatesKnown/Unknown

Information

Independent = IAssistance = AUnable = U

UsesManipulatives

Not needed = NIndependent - IAssistance = AUnable = U

CommunicatesSolutions Verbally

Independently = IWith assistance = AUnable = U

CommunicatesSolutions in

Writing

Independently = IWith assistance = AUnable = U

Score Card for What’s the Problem? Learning ExperienceStudent Name

Dia

gnos

tic S

core

Cru

nchy

Coo

kies Sweet Treats Score Circus Cents Score Building Blocks

ScoreFive

Black Squares

BookScore

*LevelDP

DvStudent Teacher Student Teacher Student Teacher

*D = Distinguished, 9-8 points P = Proficient, 7-5 points Dv = Developing, 5-0 points#/** = raw score/differentiated score

STUDENT WORK

Out of 14 students, six students scored in the distinguished level, six students scored in the proficient level, and two students scored in the developing level. All students received a raw score based on the teacher’s scoring rubric. The instruction and tasks were differentiated for lower performing students based Individual Educational Plan goals. These students were given a differentiated score.

Since introducing this activity, all of the students have used a variety of methods for solving problems. The activities include concrete and abstract reasoning as well as communicating solutions to others. In this manner, the class is exposed to a variety of mathematical concepts and applications.

The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads the way they can see this when using concrete objects. These two students have not mastered the one-to-one correspondence between number and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre-requisite skill for this learning experience.

Students who are in the proficient level can comfortably use the counters and manipulatives when they are given a longer period of time to explore written format. When given the correct tools, such as a vocabulary list of written numbers, the students can write the words. They can also explain their thinking and processing of the word problems. Drawings are more detailed and some students use tallies and simple marks to represent data. At this level the students do not always recognize that using different strategies should yield the same results.

Finally, students who received a distinguished score have the ability to use multiple representations for solving the problem without assistance from others. He or she can use numbers effectively, apply a number sentence and demonstrate the skills in an abstract format. They are able to complete the examples and clearly demonstrate their understanding by communicating to others. At this level the students recognize that using different strategies should yield the same results. These students also assisted those peers who did not understand what was being asked.

OVERALL ACTION RESEARCH ANALYSIS:For scores to improve and for more students to score at the distinguished and proficient levels the following needs to occur:

Prior to teaching this learning experience, each problem solving strategy expected for the specific population of students needs to be taught in isolation, practiced, and achieved by the students at a proficient level or distinguished level.

For students lagging behind or unable to achieve at the necessary levels, instruction and tasks, and assessment requirements need to be modified.

TEACHER COMMENTS

Student Name_______________________________________________________

This piece demonstrates (circle level): Distinguished level Proficient Level Developing Level

What this student can do What this student struggles with+ -

+ -

+ -

+ -

+ -

Additional Comments/Observations (optional):

PROCEDUREThese tasks are adapted from the Mathematical Thinking for 1st Grade unit in the Investigations in Numbers, Data and Space program. Anticipatory sets reinforce counting and writing numbers.

Task One: 1. Anticipatory Set: Read the story Ten Black What’s the Problem?.2. Distribute one black dot to each of four students who will act out mathematical

ideas from the story with manipulatives.3. Child holding one dot moves to the front of the class.4. Ask the question: How many What’s the Problem? need to be added to make a

total of 2 What’s the Problem? (1 dot)?5. Another child holding one dot comes forward and stands by the first child.6. Together students count aloud the number of What’s the Problem? in the front of

the class (2 What’s the Problem?).7. Repeat this procedure until there are 4 What’s the Problem? total. 8. To demonstrate addition have child with first dot step forward. Have the next two

children step forward and join hands with the first child to demonstrate addition of 1 + 2 = 3. Have the last child step forward and join hands with the other three children to demonstrate addition of 3 + 1 = 4. Think aloud each step of the addition procedure as a class.

9. Again identify the problem as: How many What’s the Problem? need to be added in order to make a total of 5 What’s the Problem? (adjust the number based on the level of challenge possible)? As the students think aloud the steps for solving problems and generate possible ways to solve the problem write ideas on chart paper. Ask students to identify the strategies they used to communicate the solutions.

10. Using think aloud, review steps and strategies for solving problems. Ask where in the past several activities the following occurred or could have occurred.:

Steps:1. interpret information in a word problem by underlining known

information2. draw a picture of the known information to assist in identifying the

problem3. identify the problem4. select and try possible strategies to solve the problem5. use pictures, words, and numbers to communicate the solutionStrategies: act out story problems use physical objects to

model the action in the problem

use drawings, symbols, and pictures to model the action in the problem

count by ones or grouping (tally marks)

add and subtract using number sentences

trial and error process of elimination work backwards use a t-chart make a graph use an algorithm

Task 2: Diagnostic Assessment11. Prepare and post story problem Crunchy Cookies and questions on chart paper. 12. Give students the same story problem on Crunchy Cookies Journal worksheet and

ask them to do their best to complete the worksheet. Assure them that it is ok to not know all of the answers and that they will know the answers at the end of the lesson. Explain in child-friendly terms that this is a diagnostic exercise to help you know what to teach them that they do not already know.

13. Collect the diagnostic Crunchy Cookies Journal.14. Score the journal using the What’s the Problem? Rubric.15. Record the score on Scorecard for What’s the Problem? Learning Experience.

Task 3: Teacher Modeling and Large Group Guided Practice 16. Anticipatory Set:

Prepare a box of pencils to be used for this lesson that is two less than the number of students in the room. Students count aloud the number of pencils, then count aloud the number of students.

Pose the problem: We have “x” number of pencils and “y” number of students. How many more pencils do we need so that each student has a pencil?

Explore ways of discovering the answer. Place two more pencils in the box, then distribute the pencils to each student.

17. Prepare and post story problem Missing Squares and questions on chart paper. 18. Give each student a Missing Squares Journal worksheet.19. Ask a student to read the word problem to the class. 20. Ask: #1 “What is the known information?” (5 squares). Underline the known

information on the chart paper word problem, instruct students to do the same on their worksheet.

21. Guide student practice by modeling the correct response for question #2 by drawing 5 squares under the question on the chart paper. Instruct students to draw 5 squares on Missing Squares Journal.

22. Read question #3 and instructions. Ask: “What is the problem?” and circle the information that you need to know in the word problem on the chart paper (9 squares). Students circle this information as well.

23. Read the instructions in the left box: “Solve the problem by using drawings, symbols, words or pictures to communicate a solution.” Solicit ideas from the class and draw on chart paper while students draw on their worksheets.

24. Fill in the Answer on the line provided and circle the answer.25. Model strategies for solving Missing Squares problem: by acting out, using cubes

or crackers (manipulatives), and adding.26. Ask students to complete the right box on their worksheets by choosing one of the

strategies just demonstrated by the teacher.27. Instruct students to bring journals to the floor and share their representations using

a think aloud for counting, adding and subtracting.28. Guide students in scoring their work using the What’s the Problem? rubric.29. Collect worksheets.

30. Review :Steps:1. interpret information in a word problem by underlining known


problem3. identify the problem4. select and try possible strategies to solve the problem5. use pictures, words, and numbers to communicate the solution

Strategies: act out story problems use physical objects to

model the action in the problem

use drawings, symbols, and pictures to model the action in the problem

count by ones or grouping (tally marks)

add and subtract using number sentences

trial and error process of elimination work backwards use a t-chart make a graph use an algorithm

31. Complete Teacher Observation Checklist while students are working.

Task 4: Small Group Task 32. Anticipatory set:

Set a bowl with boxes of raisins in the front of the room. Place students in groups of 3 to solve the problem Sweet Treats Journal. Ask one student from each group to come forward, count and select enough

boxed treats for each person in the group, return to the group and distribute to group members for snack while completing the task.

33. Instruct students to complete Sweet Treats Journal. Designate one person to record the group’s answers on the Sweet Treats Journal.

34. Facilitate small groups as needed.35. Allow students to work for 15 minutes.36. Students present and explain their thinking and solutions to the class using the

think aloud strategy.37. Guide the direction of the conversation by asking questions that illustrate there

may be more than one strategy for solving the problem. 38. Guide students in scoring and analyzing their work using the What’s the Problem?

rubric. 39. Collect Sweet Treats Journal worksheet. 40. Using think aloud, review steps and strategies for solving problems. Ask what

steps and strategies the students used to solve the problem.41. Complete Teacher Observation Checklist while students are working and Score

Card for What’s the Problem? Learning Experience after examining student work.

Task 5: Independent Practice

42. Anticipatory Set: Place a bowl of pennies in the front of the room. Have each student take 4 pennies from the bowl. Once students return to their seats, walk around the room and have them pay

you 3 pennies for the Circus Cents Journal worksheet. Collect and count the left over pennies.

43. Instruct students to complete the Circus Cents Journal worksheet.44. Using think aloud, review steps and strategies for solving problems. Ask what

steps and strategies the students used to solve the problem.45. Students score work with the What’s the Problem? rubric. 46. Collect Circus Cents Journal worksheet.47. Complete Teacher Observation Checklist while students are working and Score

Card for What’s the Problem? Learning Experience after examining student work.

Task 6: Independent Assessment48. Anticipatory Set: Decorate the room with blocks by letting each student build a

tower along one of the classroom walls, count the number of blocks in their tower, write the number on a piece of paper and place it on the top of their tower. Pick two towers and determine the total number of blocks, and the difference between the two.

49. Instruct students to complete the Building Blocks Journal worksheet.50. Students score work with the What’s the Problem? rubric51. Using think aloud, review steps and strategies for solving problems. Ask what

steps and strategies the students used to solve the problem. 52. Collect Building Blocks Journal worksheet.53. Complete Teacher Observation Checklist while students are working and Score

Card for What’s the Problem? Learning Experience after examining student work comparing this score with diagnostic score Crunchy Cookies Journal.

Task 7: Culminating Activity54. Anticipatory Set:

Read the teacher’s story of Four Blue Triangles which serves as an exemplar. Give students the task to discuss total number of stars in the book. Groups of 3 work on generating solutions by offering ideas such as counting,

using items, or other strategies for solving the task learned in the previous days. Give students blank sheets of paper or a modified worksheet based on their skill level.

55. Have students generate a list of where squares are found around them.56. Give each student materials to create personal book of Five Black Squares where

they add one more square on each page. (5 blank pages in book form, 5 black construction paper squares, crayons, pencils).

57. Students create and then read their books to the class.58. Pose the problem: “How many squares did you put into your book?”59. Students independently apply the strategies they just practiced to solve this

problem without counting the squares. They record the strategy(ies) on a blank

sheet of paper or modified worksheet, then meet with the teacher to review the answers using a think aloud.

60. As a class, using think aloud, review steps and strategies for solving problems. Ask what steps and strategies the students used to solve the problem.

Closure:61. In large group, discuss the strategies used in all the tasks and highlight innovative

student approaches, variety of strategies, and emphasize enduring understanding that there is more than one way to solve a problem.

62. Pose the essential question “When are some strategies better than others for solving problems?”

63. Score the self-made book with problem solving sheet using What’s the Problem? rubric.

INSTRUCTIONAL/ENVIRONMENTAL MODIFICATIONS

Students are grouped with students of varied abilities to allow for collaboration among academic levels. The teacher circulates around the room to assist students and elicit higher level thinking skills. Students are given the use of manipulatives to assist in completing the activities. Instructional modifications are provided for use with students who have individual educational plans.

Instructional/Environmental ModificationsModifications Type Specific Modification Rationale BenefitsEnvironmental and

ManagementOverview of class procedures

Preferred seating

Use of small groups

Established routines provide framework for completion of tasks (this includes procedures and rules)

Close to teacher or blackboard provides student with immediate reinforcement and allows supportive feedback

Smaller groups provide students with support from other students

Expectations have been established for proper class behaviors. All students benefit and learning can occur

Proximity control provides immediate feedback for student

Students in groups can provide additional assistance and support for students with special needs

Instructional Repeating/rephrase questions

Use of manipulatives

By providing instructional modifications, students are given the necessary assistance to complete

Students are given assistance to actively participate in these activities without being singled out as

Oral responses/taped responses to reflection questions

Modified worksheets

Pictures to show calculations

Student presentations

the tasks

Students explain their approach to solving a problem to assist them in communicating solutions

unable to complete the tasks

Students logically check answers and reasoning, strategies and skills. Struggling students may gain new insights because of peer coaching

Content/Materials Use of manipulatives such as Unifax Equation Connections

Students retell actual steps for completing tasks

Students apply higher level thinking skills to all activities.

Students are able to apply higher level skills in all problem solving situations

Tasks Math Journals are modified by using lower numbers or higher numbers depending on ability

Time allowed for the task can be lengthened or shortened depending on ability

Students complete activities based on academic abilities

Journals are created with differentiated instructions

Students work at own processing pace

MATERIALS REQUIRED FOR INSTRUCTIONSKey Reference Materials include:

Crews, Donald. Ten Black What’s the Problem?. Greenwillow Books: New York. 1986

Dacey, L. and Easton, R. Show and Tell: Representing and Communicating Mathematical Ideas in K-2. Math Solutions Publications. Sausalito: CA, 2002

Dacey, L and Easton, R. Growing Mathematically in Kindergarten. Math Solutions Publications. Sausalito. CA. 2000

.Mathematical Thinking for 1st Grade unit in the Investigations in Numbers, Data and Space program published by Scott Foresman

Websites: www.nctm.org www.emsc.nysed.gov

Classroom Supplies: Pencils

Craft Sticks (popsicle sticks) with student names Crayons Chart paper Markers Unifax Equation Connections (www.didax.com)

Materials: Ten Black What’s the Problem? Power Point Manipulatives (counting cubes) Black construction paper circles and squares (1 by 1 inch) pre-made books for creating their own books: Five Black Squares Teacher made book: Five Blue Stars What’s the Problem? Rubrics (teacher and student) Teacher Observation Math Checklist Score Card for What’s the Problem? Learning Experience Algorithm: y = .5x2+.5x where y = total number of items, x = page number Sample t-chart Sample graph Student Journal worksheets:

Crunchy Crackers for Task One Missing Squares Journal for Task Two Sweet Treat Journal for Task Three Circus Cents for Task Four Building Blocks for Task Five

TIME REQUIRED

This learning experience can be implemented over three to four days. Each activity can be completed within a scheduled math block of one hour as per the Investigations Math Program. The hour is broken into whole group activity (15-25 minutes), followed by Choice Time activities 20-30 minutes). After Choice Time, students return to the whole group setting to discuss strategies employed during Choice Time.

Planning: 45 minutes for gathering manipulatives, planning, preparing chart paper stories and journals

Implementation: Task One: Anticipatory Set: 30 minutes Task Two: Diagnostic Assessment: 15 minutes

Task Three: Teacher Modeling and Guided Practice:

45 minutes Task Four: Small Group Practice: 40 minutes Task Five: Independent Practice 30 minutes

Task Six: Independent Assessment 20 minutes

Task Seven: Culminating Activity 40 minutes Assessment: Scoring of Activity Journals: 5-10 minutes per student per worksheet

Self-Made Book and problem discussion: 5-10 minutes per student

Schedule:The Buffalo Public School’s District Math Curriculum Team requires a strict sequence for math lessons. This learning experience is designed to take place at the beginning of the school year as an introduction to basic problem solving. The skills and strategies incorporated in this learning experience will be reinforced throughout the school year. After completing this unit, students move into the unit entitled Surveys and Secret Questions when they will use problem solving skills to count, add, collect and record data.

REFLECTIONThis learning experience is created to serve as a method of scaffolding problem solving mathematical tasks for students in my class in order to promote their success at increasing levels of difficulty. The activities align to the New York State Standards as well as to the Investigations program that has been adopted by the Buffalo City School district.

My goal is to use the Standards to assess student achievement of the performance indicators as the basis for my informal observation and my formal evaluation (tasks from the Investigations Kit, teacher-made tasks). NYS Standards and Performance Indicators provide a consistent vocabulary for tasks and assessment tools making the creation of this learning experience easy to write and easier for students to understand.

The methodology for communicating mathematical thinking in this learning experience is influenced by the writings of Dacey and Easton in the book, Show and Tell: Representing and Communicating Mathematical Ideas in K-12. I encourage students to express ideas, ask questions, make presentations, peer teach and listen to each other during math time. For example, students in my class who have strengths in communicating verbally assist peers by illustrating their thinking processes aloud. The conversations help me track student learning for modifying and adjusting my lesson or for selecting students needing individual attention.

I believe the following are key reasons why I can meet my goals for improving student mathematical understanding, and why I can assess the learning standards effectively through implementing this learning experience:

I offer multiple tasks that provide exposure to individual learning styles which increases student motivation. The collection of tasks provide kinesthetic experiences such as using physical objects and acting out solutions, verbal opportunities to explain discovery of solutions, the use of mathematical formulas that express the problem solving process in a logical-mathematical approach, and reading about everyday math situations for the linguistic preference.

The technique of planning and labeling information is vital for students to solve word problems. However, we did not focus on a single word for using this skill. Students were to circle phrases that would assist them in understanding the word problems. Many of my students could identify the known and unknown information with assistance; however since using this technique, my students have become comfortable with using Plan and Label to complete independent journal activities for math.

Many of the students were able to effectively use the rubric to monitor their progress. This actively engaged students in the learning process. For example, in the first implementation, one student could not verbally explain the process for solving the problems or use pictures. In the second implementation, this same student could draw the correct number of items as well as locate the known and unknown information with assistance. In the final implementation, the student was able to verbally explain the process for solving the problem. Watching his own progress in scoring his rubric led to motivation and cognitive changes that account for his improvement.

This learning experience has undergone some changes due to the peer review process. Using feedback from other professionals assists me in making this a better product for teachers to use. The input of warm and cool comments during peer review provides a way for me to clarify those areas that are unclear for the reader and therefore maybe be unclear to the students. For example, one reviewer asked: “Is it appropriate to use the word ‘strategy’ with first grade students?” My response was “yes”. Students need to be exposed to mathematical terms from the beginning in proper context. This promotes mathematical understanding rather than the memorization of vocabulary.

Digital camera photos serve as a record of how the students completed the tasks, as well as providing me a means to show others the actual implementation of this learning experience. The digital images form a Point presentation for sharing this learning experience during peer reviews.

As well as feedback from other colleagues, I have had the opportunity to work in a study group with Jeff Arnold and Pat Loncto in revamping this learning experience. We examine the usability of this learning experience for other colleagues as we consider the comments from Peer Reviews. We refine the student worksheets to align with the NYS Performance Indicators, and we create scoring and grading tools for documenting the level of student performance.

When examining the student samples, it is clear to me that my students understand the process of applying strategies, yet many of them still need concrete materials to find the solution for word problems. The journals in this learning experience have been

implemented three times with the same group of students and the students have made progress in applying some of my goals and objectives. I was surprised at how patient the students were when asked to repeat the identical task. The repeated practice provided a foundation for growth in succeeding tasks even though they were identical. Given that the students in the class are below first grade, the progress they made demonstrates learning is taking place.

Translating performance indicators into classroom practice provides me with a uniform measurement for all the students. I discovered that I can adapt any lesson from my required curriculum and develop assessment tools because the performance indicators provide the language of my subject. My students are learning to solve problems independently using strategies that allow them to communicate correct answers and they are having fun too. That makes the work of this learning experience worth my efforts. All of the students enjoyed completing the activities and found that “doing Mrs. Kudrna’s homework was fun.”

I learned that performance indicators are more powerful to use than they are painful to sort through. I learned how important student self-assessment is for student engagement.

Name: ____________________

Crunchy Cookies Journal

You have 3 cookies. How many cookies do you need to make a total of 6?

1. Underline the known information.

2. Draw a picture to show the known information.

3. Circle the problem you need to solve in the word story above.

Solve the problem by drawing a picture. Show your work.

Choose another strategy. Show your work.

act it out use manipulative add to find answer

Answer____________Circle your answer.


Teacher Initials ______ (act it out/use of manipulatives)

Name: ______________________

Missing Squares Journal

You have 5 square crackers. How many square crackers do you need to make a total of 9?










Name _________________

Sweet Treats Journal You have 9 pieces of candy. You have 13 friends. You want to give each friend one piece of candy. How many pieces of candy will you need to make a total of 13 pieces?



3. Circle the problem that you need to solve in the word story above.

Solve the problem by using manipulatives. Show the teacher. Draw your solution.



act it out add or subtract to find answer


Teacher Initials ______ (act it out/use of


manipulatives)

Name ___________________________

Circus Cents Patrick wants to go to the circus. A ticket will cost 15 cents. He has 6 cents. How many pennies will he need to make a total 15 cents?




Name: ______________________

Building Blocks Journal

You have 4 blocks. How many blocks do you need to make a total of 7?



Solve the problem using several strategies. Show your work.

Strategy 1



Strategy 2



Strategy 3










Teacher Exemplars for Distinguished Student Work Crunchy Cookies Journal

You have 3 cookies. How many cookies do you need to make a total o



How many do you need to

to make a total of 6?

3. Circle the problem you need to solve in the word story

above.



Answer_____3_______Circle your answer.

3 + 3 = 6

1+ 1 + 1 + 1 + 1 + 1 = 6

three and three is six

Answer_____3______Circle your answer.

Teacher Initials ____CK__ (act it out/use of manipulatives)

Teacher Exemplars for Distinguished Student Work Missing Squares Journal

You have 5 squares. How many square crackers do you need to



How many do squares do you need to make nine?



Choose another strategy. Show your work. act it out use manipulative add to find answer

Answer______4______Circle your answer.

5 + 4 = 9

9 – 5 = 4

five and four are nine

Answer___4_________Circle your answer.

Teacher Initials ___CK___ (act it out/use of manipulatives)

Teacher Exemplars for Distinguished Student Work

Sweet Treat Journal You have 9 pieces of candy. You have 13 friends. You want to give each friend one piece of candy. How many pieces of candy will you need to make a total of 1How many will you need to make a total of 13 pieces?




Solve the problem by using manipulatives. Show the teacher.

Draw your solution.

(adding with manipulatives)

(subtracting with manipulatives)

(child crosses out 4 buttons)

Answer____4________Circle your answer.

Teacher Initials ___CK___ (act it out/use of manipulatives)

Choose another strategy. Show your work. act it out add or subtract to find answer

9 + 4 = 13 nine and four is thirteen

13 - 9 = 4 thirteen take away 9 is four

Comments: child did act out. See anecdotal record


Teacher Initials __CK____ (act it out/use of manipulatives)


Circus Cents Patrick wants to go to the circus. A ticket will cost 15 cents. He has 6 cents. How many pennies will he need to make a tot




Solve the problem using several strategies. Show your work.

Strategy 1(use of manipulatives)



Strategy 2(act it out)


Teacher Initials _CK_____ (act it out/use of manipulatives)

Strategy 3(use of pictures, numbers and/or words)

oooooo + ooooooooo

6 + 9 = 15

15 – 6 = 9

six and nine are fifteen

fifteen take away six is nine



How many pennies do you need to make a total of 15 cents?


Building Blocks Journal

You have 4 blocks. How many blocks do you need



3. Circle the problem you need to solve in the word story

above.




4 and 3 is 7

4 + 3 equals 7

four and three is seven

Answer_____3_______Circle your answer.

Teacher Initials _CK_____ (act it out/use of manipulatives)

How many blocks do you need to make a total of 7?

Score Card for What’s the Problem? Learning Experience

Student Name

Dia

gnos

tic S

core

Cru

nchy

Coo

kies Sweet Treats Score Circus Cents Score Building Blocks

ScoreFive

Black Squares

BookScore

*LevelDP

DvStudent Teacher Student Teacher Student Teacher

A 7 9 DB 5 6 PC 3 8 DD 9 9 DE 7 8 DF 4 5 PG 3 3/6** DV/PH 5 9 DI 6 8 DJ 2 3/7** DV/PK 3 5 PL 4 6 PM 3 6 PN 3 7 P

*D = Distinguished, 9-8 points P = Proficient, 7-5 points Dv = Developing, 5-0 points#/** = raw score/differentiat

QUESTIONS/PROBLEM AREAS ARE ITALICS AND BOLD FOR REFERENCE. NEW PARAGRAPH IS UNDER WITH CHANGES IN BOLD AND ITALICS. ALL I

NEED TO DO IS CUT AND PASTE. EACH PAGE IS NOTED FOR EASY PLACEMENT

Page 13 Student work: 3rd PARAGRAPH

Confusing sentence: Drawings however are inaccurate

The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads the way they can see this when using concrete objects. These two students have not mastered the one-to-one correspondence between number and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre-requisite skill for this learning experience.

New paragraph

The developing level student samples show that the students can not use abstract reasoning and application to compete the word problems. Therefore, instruction and tasks were differentiated to allow students to focus on mastering concrete mathematical concepts. In general, developing students have difficulty writing numbers and/or words to solve the problem. However, they can act out the story with some directions from the teacher. The students can also use manipulatives to explain their processes in solving the questions. Drawings however, are inaccurate representations of the problem and solutions because students are unable to see the math processes in their heads. When asked to explain their drawings, the students are unable to communicate the process of finding a solution to another individual. However, if they use manipulatives, students can explain the process using concrete objects as they complete the steps to find the solution. These two students have not mastered the one-to-one correspondence between number

and object when counting and a different educational goal was established. Understanding one-to-one correspondence is a pre-requisite skill for this learning experience.

Page 13 under RESEARCH FINDINGS…..

UNCLEAR TO MARY: Prior to teaching this learning experience, each problem solving strategy expected

for the specific population of students needs to be taught in isolation, practiced, and achieved by the students at a proficient level or distinguished level.

New statement

Prior to teaching this learning experience, each problem solving strategy is taught in isolation, practiced and achieved by the students at the proficient or distinguished level.

Page 15: Mary is unclear of this section and the steps…..

10. Using “think aloud”, review steps and strategies for solving problems. Ask

where in the past several activities the following occurred or could have occurred.:

Steps:1. interpret information in a word problem by underlining known


problem3. identify the problem

select and try possible strategies to solve the problem

July 14, 2006 Peer Review Comments: I DID THIS: Replace title Connecting the Dots to What’s the Problem I DID THIS: Replace Dots to What’s the Problem Read to see if all the replaces were correct and found. Add to student work section a comment on how students can be inconsistent

depending on how their day is going. State something about conferencing with them if you see ups and downs in their rubric self scoring

Modifications suggestionso Computer for one to one correspondenceo Games see UB math for example party sceneo Visual cue of plan and label worksheets with underline and circle doneo Counting jaro Writing of numbers daily practice on lined papero Create challenge problems in learning station for better students: Design a

game, make a new worksheet, use higher numbers, make posters for room Strategies suggestions: word wall Fix numbers on page 13 of student work section Need sample of teacher book Use dev, Pro, DIS for the level descriptions Student rubric level 3 add word count Page 18 step 48 too many steps? Page 18 Four Blue Stars Page 20 put in new modifications from above Page 21 Four Blue Stars Power point of lesson instructions Power point of book exemplar to discuss punctuation, etc…. Video tape teacher reading book and then the kids, take home story and video Fix book page order for developing student

Mary’s Comments

remember to do a cover sheet to tell name of le, your name ...€¦ · web viewinterpret...

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