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Key Assessment:

2nd Grade Math Concepts: Mastering the Steps of Problem Solving

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Kameron B. Williams

FRIT 7231: Instructional Design

Georgia Southern University

Spring 2014

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Part 1: Identification Of a Learning Program

General Audience

The primary audience is a class of general education 2nd grade students at Walker Park

Elementary School in Walton County, Georgia. There are 26 students enrolled in the class. These

students range in age from 7-9 years old.

!Problem Identification

It is imperative that students have the foundation needed to approach word problems with

confidence and accuracy. As standardized testing moves closer to a PARCC type assessment,

students of all ages are going to be expected to show deeper learning through the use of their

critical thinking and problem-solving skills. Math assessments developed today consist of a

majority of word problems which require deeper comprehension skills. Students must be

prepared to explain their thinking, as well as describe the steps they have taken to come to a

solution. Therefore, by the second grade, students must learn the problem solving process.

The problem solving process is a series of steps than can be used to solve a word

problem. Through formal and informal assessments of students, I have found that the majority of

second graders have trouble identifying the problem(s) presented in word problem because they

lack knowledge of the steps of problem solving. This instructional unit will consist of lessons

that teach students the steps of the problem solving process, including applicable strategies used

at each step. Learning these steps will help students guide themselves through a series of

strategies that will lead them to the problem. Furthermore, the process of working through the

problem solving steps will encourage increased comprehension and critical thinking skills.

Instructional Goals

Students will be able to:

• Break down the word problem for understanding.

• Identify the question the word problem is attempting to answer.

• Select an appropriate strategy to solve a word problem.

• Solve the problem presented within a word problem accurately.

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Part 2: Learner Analysis

Introduction

The target group of learners are 2nd grade students at Walker Park Elementary in

Monroe, Georgia. The students range in ages from 7 to 9 years old, with a median age of 8.

There are 11 girls and 15 boys in the class, including 1 boy who was retained in Kindergarten.

The class is comprised of 20 Caucasians and 6 African Americans. Of these students, 7 have

tested for and been identified as gifted and are served for two segments per day. A total of 3

students have been identified for EIP (Early Intervention Program), 1 being served for math and

2 being served for both reading and math. There are 11 students that have been labeled as

economically disadvantaged, 5 students come from single family homes, and 2 students live with

family members other than parents. As the classroom teacher of these students, I was able to

attain their demographic information through a review of registration forms, as well as by

accessing data using Infinite Campus, our school’s online campus portal, and the Statewide

Longitudinal Data System (SLDS).

!Entry Skills

• All students can read grade-level materials. • All students demonstrate basic math competencies. • All students can follow written instructions. • All students can use a computer (log in; use mouse and keyboard correctly; navigate age-

appropriate website features and links).

!Prior Knowledge

• Students have an understanding of addition, subtraction, and strategies for addition and

subtraction within 20. • Students have an understanding of whole number relationships and place value, including

grouping in tens and ones. • Students can work with a variety of problems that have unknowns in all positions. • Students can use objects, drawings, and equations to solve one-step problems.

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This information was attained by reviewing the Georgia Common Core Standards for 1st and

2nd grade students.

!Attitudes Toward Content and Academic Motivation

I conducted a survey to collect my students’ attitudes toward content and academic

motivation. Overall, second grade students enjoy math, particularly when a variety of

instructional strategies are used in a lesson. However, 9 out of 26 students recorded an aversion

to word problems. This could be due in part to the fact that this age-group is still acclimating to

the expectation that they should read instructions and word-problems independently. In first

grade, students are given the support of their teacher orally reading such information, but by

second grade they are being weaned of this assistance. By making the word problems more

relevant and showing them ways in which such skills will help them in their daily lives, the

students tend to show an increase in interest and motivation.

The students are highly motivated to learn in an online environment. They enjoy any

opportunity they can get to use the computer and have multiple opportunities during each school

week to visit educational websites consisting of a variety of learning games. Additionally, they

have extensive practice on several websites that take them through progressively challenging

learning modules in both reading and math. !Educational Ability Levels

Due to the grade-level of these students, there are no standardized test scores to refer to.

However, in the areas of both reading and math, the majority of students are on grade-level and

at least 25% of the class is functioning above grade-level. Several students are performing

slightly below grade-level and 2 students have been identified as needing remediation in math.

!General Learning Preferences

According to student responses to survey questions, they enjoy learning when a variety of

instructional strategies are used. They look forward to small group tasks and learning through

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games. All students noted enjoying using the Smart Board for interactive activities that involve

the whole group. Also, as stated previously, the students have a strong interest in the computer.

!Attitude Toward Teachers and School

The majority of students that comprise this group of learners have positive attitudes

towards school and learning. In addition, these students are respectful towards their teachers and

other members of the school staff. 2 students have had minor issues with negative feelings

towards learning and classwork; these students are performing below grade-level and struggling

in both math and reading. One below grade-level student has low motivation and has occasional

outbursts of frustration and anger which translates into negative behaviors and attitude towards

the teacher and classmates.

!Part 3: Task Analysis

Method of Analysis: Procedural

The instructional problem being addressed is that students are not taking the proper steps

necessary to solve word problems. I will identify a systematic method and process that students

need to follow to help meet learning objectives. I completed a procedural analysis because I

needed to identify the steps required by students to solve math word problems. I made a detailed

outline of the steps I usually teach to my 2nd grade students. I then worked out several sample

word problems with a small group of students in my class, following the outline I initially creat-

ed. This helped me be more specific in my procedure analysis and identify steps that I had left

out of the process.

!SME:

I am acting as the SME for the task analysis. I hold a B.S. in Early Childhood Education

and have taught in the public school system for six years. I have experience in grades Pre-K

through 3rd, with my most recent placement being in the 2nd grade. I have been teaching in a

regular education 2nd grade classroom for three years and plan units of instruction for math,

reading, science, and social studies. I have attended several professional development math cour-

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ses through the Northeast Georgia RESA and I am also a certified gifted teacher. I am currently

enrolled in my second semester of studies at Georgia Southern University working towards a

M.S. in Instructional Technology.

!!Procedure Analysis Outline:

1. Preview the problem

1. Read the problem.

2. Reread the problem slowly.

2. Understand the Problem

1. Ask yourself the following questions and use the given strategy.

1. What is the problem about?

1. Restate the problem in your own words.

2. What is the question asking?

1. Say the question using a fill-in-the-blank format.

3. What are the key terms in the problem?

1. Identify the key terms in the problem.

1. Box the key terms.

4. What information is given?

1. Identify the information given in the problem.

1. Circle the information.

5. Is there any unnecessary information?

1. Identify unnecessary information.

1. Cross out unnecessary information.

6. What are you to find?

1. Identify the question the problem is attempting to answer.

1. Underline the question.

3. Plan to solve the problem.

1. Ask yourself the following questions and write down your answers.

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1. What do the key terms tell me about the operation needed to solve the

problem?

2. What strategy can I use to solve this type of operation?

1. Draw a picture.

2. Use a number line or hundreds chart.

3. Write an equation.

1. Use a symbol for the unknown information.

4. Solve the problem.

1. Work out the problem using the strategy you have chosen.

1. Show all of your work.

2. Write your answer in a complete sentence.

1. Circle or label your answer.

5. Check your answer.

1. Ask yourself the following questions and write down your answers.

1. What strategy can I use to check my work?

1. Ask yourself if your answer makes sense.

2. Input the answer in the equation you wrote in step 3 and solve the

equation.

3. Redo your work.

!

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!

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Part 4: Instructional Objectives

Terminal Objective 1: The student will break down the word problem for understanding.

Enabling Objectives:

1A. The student will indicate who is involved in the problem.

1B. The student will indicate what is involved in the problem.

!Terminal Objective 2: Identifies the question the word problem is attempting to answer.


2A. List the key terms commonly found in word problems.

2B. Identify the key terms in the problem that indicate an addition operation is necessary.

2C. Identify the key terms in the problem that indicate a subtraction operation is necessary.

2D. Identify the number information included in the story problem.

2E. Differentiate the necessary information in a word problem from the unnecessary information.

!Terminal Objective 3: Selects an appropriate strategy to solve a word problem.


3A. Define the key terms identified in the word problem.

3B. List strategies that can be used to solve addition and subtraction problems.

3C. Select an appropriate strategy that applies to the operation needed to solve a word problem.

!Terminal Objective 4: Accurately solves the problem presented within a word problem.


4A. Apply a strategy to help solve the problem.

4B. Show the work completed in the application of a chosen strategy.

4C. Answer to the question correctly in a complete sentence.

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Classification of Instructional Objectives:

!Relationship between Instructional Objectives and Standards:

!Content

Performance

Recall Application

Fact 2D, 3A

Concept 2B, 2C

Principles 2E

Procedure 1A, 1B, 2A, 3B 3C, 4A, 4B, 4C

Interpersonal

Attitude

Instructional Objectives

Georgia Performance Standards

1 ELACC2RF3 Know and apply grade-level phonics and word analysis skills in decoding words.

ELACC2RF4 Read with sufficient accuracy and fluency to support comprehension.

1A.

1B.

2 MCC.2.OA.1 Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

2A.

2B.

2C.

2D.

2E.

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! !!!


MCC2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

MCC2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

3A. MCC.2.OA.1

3B. MCC2.OA.2

MCC2.NBT.53C.


MCC2.OA.2 Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

MCC2.NBT.5 Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

4A. MCC2.OA.2

MCC2.NBT.54B.

4C. MCC.2.OA.1

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Part 5: Development of Assessments

Instructional Strategies

Goals Objectives UDL Assessments

Lesson 1: Reading for Understanding

The student will identify the “who” and “what” involved in a story problem by dragging them to an appropriate box on the screen.

Terminal Objective 1: The student will break down the word problem for understanding. Objective 1A: The student will indicate who is involved in the problem. Objective 1B: The student will indicate what is involved in the problem.

Multiple Means of Representation (read problems independently or listen to them read aloud; picture cues used to assist decoding and comprehension); Multiple Means of Action and Expression (physical actions engage student)

Learners will take a quiz in which they must identify the “who” and “what” that is involved in a series of story problems.

Lesson 2: What’s the Problem?

The student will label the components of a story problem.

Terminal Objective 2: The student will identify the question the word problem is attempting to answer. Objective 2B: The student will identify the key terms in the problem that indicate an addition operation is necessary. Objective 2C: The student will identify the key terms in the problem that indicate a subtraction operation is necessary. Objective 2D: The student will identify the number information included in the story problem. Objective 2E: The student will differentiate the necessary information in a word problem from the unnecessary information.

Multiple Means of Engagement (key words, explanations, and pictures support concepts and encourage student engagement and understanding; embedded comments and hints); Multiple Means of Action and Expression (physical actions engage student)

The learner will modify a document by dragging specified symbols to label and identify the parts of a series of word problems.

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Lesson 3: What’s My Strategy?

The student will match story problems with correctly executed strategies.

Terminal Objective 3: The student will select an appropriate strategy to solve a word problem. Objective 3A: The student will define the key terms identified in the word problem. Objective 3B: The student will list strategies that can be used to solve addition and subtraction problems. Objective 3C: The student will select an appropriate strategy that applies to the operation needed to solve a word problem.

Multiple Means of Engagement (option to choose from two correct strategies, allowing students to execute individual choice and autonomy)

Using the website, www.edu.glogster.com, the learner will create an online poster displaying their knowledge of strategies that can be used to solve a word problem.



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!!!The assessments that I have designed are performance based assessments. I want students to

demonstrate the skills they have learned from the online module. To accurately complete these

tasks, students must apply their knowledge of the problem solving process.

Lesson 4: Solve It!

The student will solve for and arrive at a correct answer to a story problem by applying a chosen strategy.

Terminal Objective 4: The student will solve the problem presented within a word problem accurately. Objective 4A: The student will apply a strategy to solve the problem. Objective 4B: The student will show the work completed in the application of a chosen strategy. Objective 4C: The student will answer the question correctly in a complete sentence.

Multiple Means of Representation (vocabulary and mathematical symbols clarified using labels and embedded hints; options for comprehension provided through the use of cues, prompts, and interactive models; access to the initial part of the lesson at multiple entry points); Multiple Means of Engagement (option to apply choice of strategies in solving the problems, allowing them to execute individual choice and autonomy)

The learner will take a quiz in which they must solve a series of word problems using what they know about the problem solving steps. For each problem, they are asked to label important words and use a strategy to solve the problem. They must show your work and answer the problem in a number sentence and a written sentence.



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Objective 1: The student will break down the word problem for understanding.

Objective 1A: The student will indicate who is involved in the problem.

Objective 1B: The student will indicate what is involved in the problem.

!Assessment: Learners will take a quiz in which they must identify the “who” and “what” that is

involved in a series of story problems.

UDL Principle: This quiz can be offered in both a fill-in-the-blank format as well as a multiple

choice format. Doing so will follow the principle of multiple means of expression, as students

will be provided various methods to respond.

!Objective 1 Assessment:

Directions: Read each story problem. Answer the questions following each problem.

1. Sam and Tina went shopping at the mall. Sam spent $12 on a t-shirt and Tina spent $5 on a

pair of earrings. How much money did Sam and Tina spend altogether?

A. Who is involved? Sam and Tina

B. What is involved? Sam and Tina’s money

2. Kim and Danny had a garage sale. They made $25 on Saturday and $10 on Sunday. How

much more money did Kim and Danny earn on Saturday?

A. Who is involved? Kim and Danny

B. What is involved? Kim and Danny’s money

3. Nick has 11 stickers. 4 of his stickers are smelly. Stacy has 7 stickers less than Nick. How

many stickers does Stacy have?

A. Who is involved? Nick and Stacy

B. What is involved? stickers

4. Mac has 14 toy cars. His brother takes away 7 of his toy cars. How many cars does Mac have

now?

A. Who is involved? Mac and his brother

B. What is involved? toy cars

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5. Jeff has 13 pencils. 3 of his pencils are sharpened. Jeff gives his sister 5 pencils. How many

pencils does Jeff have left?

A. Who is involved? Jeff and his sister

B. What is involved? pencils

6. Bill went to a pet shop. He bought 15 gold fish and 7 blue fish. How many fish did he buy in

all?

A. Who is involved? Bill

B. What is involved? gold fish and blue fish

7. Joe and Ted went fishing at the lake. Joe caught 4 fish and Ted caught 7 fish. How many

more fish did Ted catch than Joe?

A. Who is involved? Joe and Ted

B. What is involved? fish

8. Shane read 9 pages of his book yesterday. Today, he read 11 pages. What is the total number

of pages that Shane read?

A. Who is involved? Shane

B. What is involved? the pages he read

9. Linda has 12 candies. Chloe has 7 candies. 2 of Chloe’s candies are sour. How many candies

do they have in all?

A. Who is involved? Linda and Chloe

B. What is involved? candies

10. Tony picked up 12 shells at the seashore in the morning and 7 shells in the afternoon. How

many shells did he pick up in all?

A. Who is involved? Tony

B. What is involved? seashells

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Lesson 1 Assessment Rubric:

• Above expectations: Student completes assessment with 2 or less errors. (90% or higher)

• Demonstrates clear understanding: Student completes assessment with 3-4 errors. (80-89%)

• Demonstrates some understanding: Student completes assessment with 5-6 errors. (70-79%)

• Understanding not satisfactory: Student completes assessment with 7-8. (60-69%)

• Little to no understanding evident: Student makes 9 or more errors; student makes no

attempt. (59% or less)

!!

Lesson 2: What's the Problem?

Objective 2: The student will identify the question the word problem is attempting to answer.

Objective 2A: The student will list the key terms commonly found in word problems.

Objective 2B: The student will identify the key terms in the problem that indicate an

addition operation is necessary.

Objective 2C: The student will identify the key terms in the problem that indicate a

subtraction operation is necessary.

Objective 2D: The student will identify the number information included in the story

problem.

Objective 2E: The student will differentiate the necessary information in a word problem

from the unnecessary information.

!Assessment: The learner will modify a Word document in which they identify the parts of a

series of word problems.

UDL Principle: This assessment follows the principle of multiple means of representation, as it

provides options for comprehension. It does so by having students high light the parts of a word

problem with clearly defined symbols. This helps them to differentiate the important information

from the irrelevant information.

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Objective 2 Assessment:

Students will work through a series of ten word problems.

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!Lesson 2 Assessment Rubric:

• Above expectations: Student accurately labels 9 or more word problems. (90% or higher)

• Demonstrates clear understanding: Student accurately labels 8 word problems. (80%)

• Demonstrates some understanding: Student accurately labels 7 word problems. (70%)

• Understanding not satisfactory: Student accurately labels 6 word problems. (60%)

• Little to no understanding evident: Student accurately labels 5 or less word problems. (50%

or less)

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Lesson 3: What's My Strategy?

Objective 3: The student will select an appropriate strategy to solve a word problem.

Objective 3A: The student will define the key terms identified in the word problem.

Objective 3B: The student will list strategies that can be used to solve addition and

subtraction problems.

Objective 3C: The student will select an appropriate strategy that applies to the operation

needed to solve a word problem.

!Assessment: The learner will create an online poster displaying various strategies that can be

used to solve a word problem. The website they will use is www.edu.glogster.com. Students will

have the option to choose one word problem and must show at least three different strategies on

their poster that can be used to help solve the problem.

UDL Principle: This assessment follows the principles of multiple means of representation and

engagement. The Glogster online poster maker offers numerous customization options and

allows for the inclusion of audio and video files. Students can show their knowledge of addition

and subtraction strategies in a variety of ways, thus they are being given varied options for

perception and comprehension.

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Objective 3 Assessment: Using the website, www.edu.glogster.com, the learner will create an

online poster displaying various strategies that can be used to solve a word problem.

!Sample finished product:

!!!!!!!!!!!!!!!!!Lesson 3 Assessment Rubric:

• Above expectations: Student accurately demonstrates 4 or more strategies.

• Demonstrates clear understanding: Student accurately demonstrates 3 strategies.

• Demonstrates some understanding: Student accurately demonstrates 2 strategies.

• Understanding not satisfactory: Student accurately demonstrates 1 strategy.

• Little to no understanding evident: Student fails to accurately demonstrate a strategy; student

makes no attempt.

!

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Lesson 4: Solve It!

Objective 4: The student will solve the problem presented within a word problem accurately.

Objective 4A: The student will apply a strategy to solve the problem.

Objective 4B: The student will show the work completed in the application of a chosen

strategy.

Objective 4C: The student will answer the question correctly in a complete sentence.

!Assessment: The learner will take a quiz in which they must solve a series of word problems

using their choice of strategies.

UDL Principle: This assessment follows the principle of multiple means of expression, as

students will have the option to decide upon their choice of strategy to help them solve a series of

word problems.

!Objective 4 Assessment:

Directions: Using what you know about the problem solving steps, solve the following problems.

Remember to label important words and use a strategy to help you solve the problem. You must

show your work and answer the problem in a number sentence and a written sentence.

1. Sam and Tina went shopping at the mall. Sam spent $12 on a t-shirt and Tina spent $5 on a

pair of earrings. How much money did Sam and Tina spend altogether?

Answer: $12 + $5 = $17; Sam and Tina spent $17 altogether.

2. Kim and Danny had a garage sale. They made $25 on Saturday and $10 on Sunday. How

much more money did Kim and Danny earn on Saturday?

Answer: $25 - $10 = $15; Kim and Danny earned $15 more on Saturday.

3. Nick has 11 stickers. 4 of his stickers are smelly. Stacy has 7 stickers less than Nick. How

many stickers does Stacy have?

Answer: 11 - 7 = 4; Stacy has 4 stickers.

4. Mac has 14 toy cars. His brother takes away 7 of his toy cars. How many cars does Mac have

now?

Answer: 14 - 7 = 7; Mac has 7 cars now.

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5. Jeff has 13 pencils. 3 of his pencils are sharpened. Jeff gives his sister 5 pencils. How many

pencils does Jeff have left?

Answer: 13 - 5 = 8; Jeff has 8 pencils left.

6. Bill went to a pet shop. He bought 15 gold fish and 7 blue fish. How many fish did he buy in

all?

Answer: 15 + 7 = 22; Bill bough 22 fish in all.

7. Joe and Ted went fishing at the lake. Joe caught 4 fish and Ted caught 9 fish. How many

more fish did Ted catch than Joe?

Answer: 9 - 4 = 5; Ted caught 5 more fish than Joe.

8. Shane read 9 pages of his book yesterday. Today, he read 11 pages. What is the total number

of pages that Shane read?

Answer: 9 + 11 = 20; Shane read a total of 20 pages.

9. Linda has 12 candies. Chloe has 7 candies. 2 of Chloe’s candies are sour. How many candies

do they have in all?

Answer: 12 + 7 = 19; Linda and Chloe have 19 candies in all.

10. Tony picked up 12 shells at the seashore in the morning and 5 shells in the afternoon. How

many shells did he pick up in all?

Answer: 12 + 5 = 17; Tony picked up 17 shells in all.

Lesson 4 Assessment Rubric:

14-15 points: Exceeds; 12-13 points: Meets standard; 11 points: Approaching standard; <11 points: Does not meet standard

! Demonstrates clear understanding

3 points

Demonstrates some understanding

2 points

Understanding not satisfactory

1 point

Labels important words Important words are labeled. Important words are not all labeled.

Important words are not labeled.

Strategy The strategy used matches the problem correctly.

A strategy was used but does not match the problem.

No strategy is used.

Number sentence The math problem is written correctly.

The math problem is mostly written correctly.

The math problem is not written.

Complete sentence The answer is stated in a complete sentence.

The answer is stated in an incomplete sentence; the

sentence written does not match the problem.

The answer is not stated in a written sentence.

Answer The answer to the math problem is correct.

The answer is correct but does not match the word problem.

The answer is wrong or not present.

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Part 6: Instructional Sequence

!!This sequence builds on concepts in a learning-related sequencing. Each lesson teaches skills that

will be required and performed in the subsequent lesson. The lessons progress from fairly simple

tasks to more challenging tasks.

!Lesson 1: Reading for Understanding

Objective 1: The student will break down the word problem for understanding.

Objective 1A: indicate who is involved in the problem.

Objective 1B: indicate what is involved in the problem.

!Initial Presentation: At the start of the lesson the students will be reminded of two reading

strategies that will help them increase their understanding; these are reading the problem slowly

and reading it a second time to increase their familiarity with it. The lesson will then begin with

the presentation of a sample story problem. The sample will be read aloud and the questions of

who and what is involved will be asked. The answers to these questions will then be highlighted

within the sample story problem. Three sample questions will be presented. The students will

then be presented with a series of ten story problems. (Ifenthaler, 2012)

Differentiation: The lesson will provide multiple means of representation by allowing students to

read the story independently and also listen to it being read aloud. Picture cues can also be used

in the story problem to assist learners who are having difficulty decoding or comprehending the

text. (CAST, 2011)

Sequence Description Objective

1 Break down a word problem and indicate who and what is involved in the problem.

1

2 Identify the question the word problem is attempting to answer. 2

3 Select an appropriate strategy to solve a word problem. 3

4 Solve the problem presented within a word problem accurately. 4

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Generative Strategy: Students must read each problem independently and then listen to it being

read aloud to them. Then, they will drag the “who” of the story problem and the “what” of the

story problem to a clearly marked box on the screen. (Ifenthaler, 2012)

Differentiation: The lesson will provide multiple means of representation by allowing students to

read the story independently and also listen to it being read aloud. Also, the lesson provides an

opportunity for physical action which supports the UDL concept of providing multiple means of

action and expression. The action of dragging the “who” and “what” out of the story allows

students to engage with the problem and better visualize what it is about. (CAST, 2011)

!Lesson 2: What's the Problem?

Objective 2: The student will identify the question the word problem is attempting to answer.

Objective 2A: identify the key terms commonly found in word problems.

Objective 2B: identify the key terms in the problem that indicate an addition

operation is necessary.

Objective 2C: identify the key terms in the problem that indicate a subtraction operation is

necessary.

Objective 2D: identify the number information included in the story problem.

Objective 2E: differentiate the necessary information in a word problem from the

unnecessary information.

!Initial Presentation: The lesson will begin with a review of addition and subtraction key terms.

Students will see the key terms along with a brief explanation and picture to match. Five sample

questions will be presented that students can interact with to identify key terms. During the

presentation of the sample story problems, students will be asked whether each problem is

addition or subtraction. (Santos-Trigo, 1998)

Differentiation: This lesson provides multiple means of representation by including not only the

key words, but also explanations and pictures to support the concepts and encourage student

engagement and understanding. (CAST, 2011)

Generative Strategy: Students must answer a “How do you know?” question by identifying the

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key term(s) in the problem. They will do so by dragging a box around key terms. Next, students

will be provided a word bank and must drag key terms into the appropriate category of story

problem, addition or subtraction. (Santos-Trigo, 1998)

Differentiation: Multiple means of action and expression are supported in this lesson. Also, the

addition of embedded comments and hints will assist students with finding relevant information.

(CAST, 2011)

!Initial Presentation: A sample story problem will be presented. The story problem will be read

aloud and the instructions for identifying key terms and information will be given and

demonstrated. A series of interactive samples will be provided. Students will be given a series of

ten story problems to interact with. (Santos-Trigo, 1998)

Plan for Differentiation: Embedded comments and hints will assist students with finding

relevant information. (CAST, 2011)

Generative Strategy: For each problem, students will be asked to put a box around key terms, put

a circle around the numerical information, put an X on unnecessary information, and underline

the question the problem is attempting to answer. The interactive elements will be provided on

the screen to be dragged onto the story problem. (Santos-Trigo, 1998)

Differentiation: Embedded comments and hints will assist students with finding relevant

information. Multiple means of engagement are supported in this lesson. Also, the lesson

provides an opportunity for physical action which supports the UDL concept of providing

multiple means of action and expression. (CAST, 2011)

!Lesson 3: What's My Strategy?

Objective 3: The student will select an appropriate strategy to solve a word problem.

Objective 3A: The student will define the key terms identified in the word problem.

Objective 3B: The student will list strategies that can be used to solve addition and

subtraction problems.

Objective 3C: The student will select an appropriate strategy that applies to the operation

needed to solve a word problem.

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!Initial Presentation: This lesson will begin with a review of strategies that can be used to assist

students in answering addition and subtraction problems. The strategies discussed will include

drawing a picture, using a number line, writing a number sentence (equation), and using a

symbol for unknown information. A series of worked examples will be presented. Next, students

will be given a set of story problems with which they must match a correctly executed strategy.

(van Loon-Hillen, 2012)

Differentiation: The UDL principles of providing multiple means of engagement is supported in

this lesson. Furthermore, the strategies presented are age and ability appropriate which optimize

relevance for learners. (CAST, 2011)

Generative Strategy: Each story problem will include four strategies, two of which are correctly

executed. Students must bubble in the circle next to their choice of correct strategies. (Santos-

Trigo, 1998)

Differentiation: The lesson supports the UDL principle of multiple means of engagement.

Students are given the option to choose from two correct strategies, allowing them to execute

individual choice and autonomy. (CAST, 2011)

!Lesson 4: Solve It!

Objective 4: The student will solve the problem presented within a word problem accurately.

Objective 4A: The student will apply a strategy to solve the problem.

Objective 4B: The student will show the work completed in the application of a chosen

strategy.

Objective 4C: The student will answer the question correctly in a complete sentence.

!Initial Presentation: The lesson will begin with a review of the previous lesson's objectives.

Students will be asked to drag the problem solving steps into correct order. Then, students will be

walked through all of the problem solving steps and shown two complete story problem

examples, one addition and one subtraction. Next, students will be given a series of ten story

problems to work on.(van Loon-Hillen, 2012)

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Differentiation: The UDL principle of providing multiple forms of representation is supported in

this lesson as vocabulary and mathematical symbols will be clarified using labels and embedded

hints. Also, options for comprehension are provided through the use of cues and prompts as well

as by providing interactive models. Students will also be able to access the initial part of the

lesson at multiple entry points. (CAST, 2011)

Generative Strategy: For each problem, students will be expected to complete all of the problem

solving steps, just as the previous lessons have taught. Students must also apply their chosen

strategy to solve for and arrive at a correct answer to the problem. Students will be given

multiple-choice format questions to prove their understanding. (Pedaste, 2006)

Differentiation: The lesson supports the UDL principle of multiple means of engagement.

Students are given the option to apply their choice of strategies in solving the problems, allowing

them to execute individual choice and autonomy. (CAST, 2011)

!!!!!!!!!!!!!!!!!!!!!!!!!

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Part 7: Design of Instruction




The student will identify the “who” and “what” involved in a story problem by dragging them to an appropriate box on the screen.

Terminal Objective 1: The student will break down the word problem for understanding. Objective 1A: The student will indicate who is involved in the problem. Objective 1B: The student will indicate what is involved in the problem.

Multiple Means of Representation (read problems independently or listen to them read aloud; picture cues used to assist decoding and comprehension); Multiple Means of Action and Expression (physical actions engage student)

Learners will take a quiz in which they must identify the “who” and “what” that is involved in a series of story problems.

Lesson 2: What’s the Problem?

The student will label the components of a story problem.

Terminal Objective 2: The student will identify the question the word problem is attempting to answer. Objective 2B: The student will identify the key terms in the problem that indicate an addition operation is necessary. Objective 2C: The student will identify the key terms in the problem that indicate a subtraction operation is necessary. Objective 2D: The student will identify the number information included in the story problem. Objective 2E: The student will differentiate the necessary information in a word problem from the unnecessary information.

Multiple Means of Engagement (key words, explanations, and pictures support concepts and encourage student engagement and understanding; embedded comments and hints); Multiple Means of Action and Expression (physical actions engage student)

The learner will modify a document by dragging specified symbols to label and identify the parts of a series of word problems.

Page ! of !29 34

Lesson 3: What’s My Strategy?

The student will match story problems with correctly executed strategies.

Terminal Objective 3: The student will select an appropriate strategy to solve a word problem. Objective 3A: The student will define the key terms identified in the word problem. Objective 3B: The student will list strategies that can be used to solve addition and subtraction problems. Objective 3C: The student will select an appropriate strategy that applies to the operation needed to solve a word problem.

Multiple Means of Engagement (option to choose from two correct strategies, allowing students to execute individual choice and autonomy)

Using the website, www.edu.glogster.com, the learner will create an online poster displaying their knowledge of strategies that can be used to solve a word problem.



Page ! of !30 34

!!!!!

Lesson 4: Solve It!

The student will solve for and arrive at a correct answer to a story problem by applying a chosen strategy.

Terminal Objective 4: The student will solve the problem presented within a word problem accurately. Objective 4A: The student will apply a strategy to solve the problem. Objective 4B: The student will show the work completed in the application of a chosen strategy. Objective 4C: The student will answer the question correctly in a complete sentence.

Multiple Means of Representation (vocabulary and mathematical symbols clarified using labels and embedded hints; options for comprehension provided through the use of cues, prompts, and interactive models; access to the initial part of the lesson at multiple entry points); Multiple Means of Engagement (option to apply choice of strategies in solving the problems, allowing them to execute individual choice and autonomy)

The learner will take a quiz in which they must solve a series of word problems using what they know about the problem solving steps. For each problem, they are asked to label important words and use a strategy to solve the problem. They must show your work and answer the problem in a number sentence and a written sentence.



Page ! of !31 34

Part 8: Plan for Formative Evaluation

Following the completion of the online module, I plan to collect the learner evaluation by

having my students complete a survey. I would also approach my four colleagues that work in

the 2nd grade and ask them to work through the module and serve as peer-reviewers. I would

then give them a survey to complete.

!Student Survey:

1. Circle the words that describe how you feel about the online module:

happy good bad frustrated excited bored interested hard

2. Compared to a regular classroom lesson, how helpful was the online module in teaching

you about the problem solving steps? (Circle one)

Better About the Same Not as Good

3. Now that you have finished the online module, how likely is it that you will use the prob-

lem solving steps when solving word problems? (Circle one)

Very Unlikely Unlikely Maybe Probably Definitely

4. How important do you think it is to use the problem solving steps? (Circle one)

Not important Kind of Important Important Very Important

5. What did you enjoy most about the module?

6. What did you enjoy least about the module?

!!

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Peer-Reviewer/SME Survey:

1. Circle the words that describe how you feel about the online module:

happy good bad frustrated excited bored interested

useful worthless

2. Compared to a regular classroom lesson, how helpful do you feel the online module

would be in teaching students the problem solving steps? (Circle one)

Better About the Same Not as Good

3. How likely do you feel the module will improve students’ use and understand of the

problem solving steps? (Circle one)

Very Unlikely Unlikely Maybe Probably Definitely

4. How important do you think it is to use the problem solving steps? (Circle one)

Not important Kind of Important Important Very Important

5. What do you feel is the most effective component or lesson of the online module? Please

explain.

6. What do you feel is the least effective component of the online module? Please explain.

7. What is your general reaction to the online module? Please elaborate on your opinion of

the subject matter and objectives, the way the course was presented, levels of required par-

ticipation, and your perceived value of the online module.

!!!

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Following the completion of both student and SME surveys, I would evaluate the data

using a qualitative analysis. This will allow me to gain insight into the participants reactions and

impressions of the online module. This process would require me to interpret survey responses

and extract major themes by calculating the number of identical and similar answers. Data might

then be organized by individual questions and answers and represented in a chart or graph to al-

low for a visual representation of results. I would further review the written responses and com-

ments and approach necessary revisions to my design based on survey input.

!!!!!!!!!!!!!!!!!!!!

!

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References

CAST (2011). Universal design for learning guidelines version 2.0. Wakefield, MA: Author.

Retrieved from http://www.udlcenter.org/aboutudl/udlguidelines

Ifenthaler, D. (2012). Determining the effectiveness of prompts for self-regulated learning in

problem-solving scenarios. Journal Of Educational Technology & Society, 15(1), 38-52.

Morrison, Gary R. (2012) Designing effective instruction (7th ed.). Hoboken, NJ: John Wiley &

Sons.

Pedaste, M. T. (2006). The factors influencing the outcome of solving story problems in a web-

based learning environment. Interactive Learning Environments, 14 (2), 153-176.

Santos-Trigo, M. (1998). Instructional qualities of a successful mathematical problem-solving

class. International Journal Of Mathematical Education In Science & Technology, 29 (5),

631.

van Loon-Hillen, N. (2012). Effects of worked examples in a primary school mathematics

curriculum. Interactive Learning Environments, 20(1), 89-99.

!!!!!

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