adding and subtracting positive and negative integers instructional program

7/28/2019 Adding and Subtracting Positive and Negative Integers Instructional Program

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Name of Student: 7th Period Resource Class (10 students)

Initiator:Jami Shlensky

Context for Instruction:

Instruction will take place at Central High School in a resource classroom. It will

occur between the hours of 1:35 and 2:25 when within the daily resource activity and

worksheet, I instruct the class on positive and negative integers. The classroom teacher as

well as a teachers aide is in the room. The class works on the daily resource assignments in

a variation of whole group instruction and independent work, depending on the task at

hand. The materials that are used include a SMART board and worksheets. Students are

seated at desks in pairs that all face the SMART board at the front of the room.

Program Objective:

When presented with the seven types of adding and subtracting positive and negative

integers (positive + positive, negative + positive & positive + negative, negative + negative,

positive positive, positive negative, negative positive, negative positive) students

will provide the correct answer to the respective equation, by writing the sum or difference

on their paper, on 8 out of 10 consecutive opportunities.

Generalization:

In order to make sure that students are generalizing the skill of using a number line

when adding and subtracting positive and negative integers, after they have a grasped the

concept of a number line with rational numbers, I will insert addition and subtraction

problems that include variables such as x and y. This will ensure that they are not

memorizing facts but actually under the concept of moving more negative or more

positive.

Rationale:

Learning how to properly add and subtract is essential to the students successes in

math. The students lack knowledge on basic properties of integers and therefore are not


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able to correctly complete higher level thinking problems. The students are stuck on the

basic addiction and subtraction of positive and negative numbers and as a result they

cannot properly grasp further concepts that they have the potential to understand. If I can

give the students a tool to mitigate their difficulty with mentally moving further positive or

further negative when adding and subtracting then they will be able to apply this

knowledge towards further learning.

Assessment Procedures:

In order to assess the students on adding and subtracting positive and negative integers,

this procedure should be followed:

1. Hand out assessment to students. Assessments will contain problems using theseven types of adding and subtracting positive and negative integers.

2. Give verbal directions to complete the problems on the worksheet. No calculatorsare to be used.

3. When students indicate they are finished, collect assessment.4. Grade assessment, out of seven.5. Chart and Graph results

o Record how many correct student received out of seven**Do not prompt or positively reinforce during assessment

Assessment Schedule:

Assess all 7 types of problems on Thursdays. I will teach on Monday, Tuesday, andWednesday and assess Thursday of every week.

Instructional Procedures:

Forward chaining will be used to teach how to add and subtract positive and negative

integers. One step will be introduced at a time to reduce the amount of time required for aninstruction session, and increase probability of correct student responses. For the steps not

yet instructed upon, the instructor should assist the student in complementing these steps

by doing them for the students on the SMART board, explaining each step verbally as it is

completed. Each step should be instructed upon for three consecutive sessions. After the

three instructional days and the assessment, the next step in the process should be

instructed upon.


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The process follows these steps:

1. Draw a number line, label it from -10 to 102. Put your finger or pencil on the first integer in the equation3. Determine if the operation and the sign of the second integer make your movement

positive or negative

4. If the movement is positive, think to move right, if the movement is negative, thinkto move left

5. Figure out the number of units you need to move based upon the second integer6. Move your finger or pencil to the right or left the necessary amount of units7. Note where your finger or pencil is, that is the solution

Stimulus Promptso No stimulus prompts are introduced at the beginning of instructing upon

a target procedure but if error patterns are noted, highlighting the error,

as followed, may be used to prevent errors.

Provide student with a note card with the target step on it writtenin black and the error highlighted. For example if student is

struggling with which way to move on the number like for positive

I would provide them with a note card that has a number line in

black and color coated for which direction is positive and negative.

Response Promptso With chaining, the previous step becomes the response prompt. No

additional response prompts are provided

Reinforcement:

Within group instruction, if a student offers the correct response they will receive

specific, direct verbal praise such as Nice T, thats the right step. First we need to draw a

number line. After three days of instruction on a specific chain, it will no longer be

positively reinforced. If at any time performance falls, reinforcement of previous steps can

be returned to and faded again until performance is stabilized.


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Maintenance:

Once criterion for mastery has been met and the material has been generalized, a

maintenance probe will be taken every two weeks. The presence of proper addition and

subtraction of positive and negative integers should also be monitored within other math

strategies and students general education classroom math assignments.


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Research Rationale

The Altiparmak and zdoan article covered the concept of teaching negative

numbers and effectiveness of a number line as a strategy. The experiment had a control

group that taught the concept of negative numbers without the number line strategy while

the experimental group was instructed to use a number line to grasp negative numbers.

The experimental group outperformed the control group. The results of this study

demonstrates that the strategy of teaching students to use a number line increases their

understanding of positive and negative integers, which will help with their accuracy in

adding and subtracting positive and negative integers. The Gunderson, Ramirez, Beilock,

and Levine article covered the relationship between spatial skill and success in

mathematics and science. Childrens spatial skill is a predictor for their ability to

understand numbers. The article stated that the success of a students number line

knowledge can be representative of their numerical understanding. This confirms the

positive relationship between number lines and mathematical understanding.

References

Altiparmak, K., & zdoan, E. (2010). A study on the teaching of the concept of negative

numbers. International Journal Of Mathematical Education In Science And

Technology, 41(1), 31-47.

Gunderson, E. A., Ramirez, G., Beilock, S. L., & Levine, S. C. (2012). The Relation BetweenSpatial Skill and Early Number Knowledge: The Role of the Linear Number

Line. Developmental Psychology, 48(5), 1229-1241. doi:10.1037/a0027433


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Blank Data Sheet

plus if

correct,

minus ifincorrect, x

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Data and Aimline

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Number

Sense

Knowledge of numbers and meaning 1-10

Knowledge of positive and negativenumbers

Understanding ofNumber line

Understanding of basic operations,

addition and subtraction

Adding and subtracting

positive and negative

integersApplication to

all types of

mathematics


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adding and subtracting positive and negative integers instructional program

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