Science Lesson Adaptation for a Special Needs Student Coursework

Danvion is a 7^th-grade boy and is suffering from the problem of foretold learning disability. He is included in the general education Mathematics class where this lesson took place. A Paraeducator supports Danvion with Individual Education Plans. The remaining Twenty-one (21) students are 7^th graders who only receive services through general education. The students are from poor economic background, most of the students are of single parented. There are 12 girls and 10 boys. The class is of mixed ability students with different backgrounds. Some students are of learning disability and are considered as nuisance in the class room. The general education Mathematics teacher has a graduate degree in math and has been teaching at the secondary level for 10 years. She has a child with a learning difficulty and believes strongly in full inclusion of students with disabilities. The paraeducator has been serving students with disabilities for five years. Following the article special education I have designed a lesson plan on Decimal System based on simple modifications to help the students who are suffering from disabilities in the regular class room. Such modifications leave a positive effect on them.

Characteristics of Danvion disability include slow process of learning, digests new information slowly, gets distracted very easily, and is slow in handling, storing, and recalling information. His strengths include working with peers, a desire to do well, and his ability to attend to the assigned tasks. His needs include frequent repetition of the concepts with more clarity and consistency, as well as continuing to develop his mathematical skills. He responds well to playing lesson games in the form of an activity.

Lesson Design, Proposed Instruction and Assessment

The basic mechanism of this lesson include students doing activities to understand what a decimal represents, viewing and observing a decimal chart, learning the concept through activities and so on. At the end of the lesson, students will be assessed based on their answers to five specific questions and the key concepts from the lesson The questions on the work sheet will evaluate the student’s knowledge to understand decimals. This lesson is designed to accommodate the student who is suffering from learning disabilities related to addition. It would be helpful to the students to solve problems on Decimal System. I will design the activities to assess the performance of the students, and through these activities I would be able to identify the problems faced by students while learning the topic, so that remedial teaching can be provided. Students know something about Decimal system. But they face the problem of speed to add big figures. Thus most of the students are unable to tackle the problems related to decimal system.

The Colorado Model Content Standards that this lesson addresses include Mathematics Standards One and Four. Mathematics Standard One states that students will apply the process of problem solving, learn to communicate mathematically, learn to reason mathematically, and make mathematical connections. The lesson addresses this standards with consistency, flexibility and various approaches through regular reinforcements and frequent revisions.

Students learn to communicate mathematically in problem situations where they can read, write and discuss ideas in a mathematical language. The lesson addresses this standard by teaching students how to communicate their ideas and thus learn to clarify, consolidate and refine their thinking and be good problem solvers. Students develop the concept of a number and decimal system relationship in situations like problem solving and communicate the reasoning used in these problems. To meet these standards, the students will construct and interpret number meanings using a decimal notation through examples from daily life, and the use of hand on materials. Demonstrate decimal notation making connections to the lesson using physical materials and technology in problem solving situations.

Lesson Delivery

The lesson on decimals will begin by activating students’ background knowlwedge about decimals. Students are weak in Math. To arouse their interest in decimal system I will illuminate them about the history of Decimal System. I will make clear to them that the Arab numeral system is considered as one of the best significant developments in Mathematics. Several theories have been advanced about its origin. Some theories tell us that the idea of decimal system was originated in China. Some suggest that the inspiration was put forward by a Muslim scientist Al-Khwarizmi. Few clarify that the decimal system was invented in the ancient Middle East. Some suggest that the Arabic numeral system is a westward transmission of the Indian numeral system.

In a decimal system there is a particular way of writing numbers. Using ten basic numbers, one can write any number in a decimal system. These basic symbols are the key factors of mathematics. Decimal system is a technique of writing numbers. Any number, from enormous amounts to tiny fractions, can be written in the decimal system using only the ten basic symbols 1, 2, 3, 4, 5, 6, 7.

The main blueprint of the lesson is to help students to learn more about Decimal system through activity based learning. Decimal system is common to all classes. Math is something you cannot rote learn. You have to understand the basic concept behind each topic. Teaching decimals is quite different as compared to other arithmetic concepts. Sometimes it is meaningless to have too many decimal places in a decimal. Since boys love cars so I will begin my lesson taking an example of a car. I will place few questions regarding the speed of the car to arouse their interest, for example:

How fast does your car run? What is the speed of your car? Do we tell the speed of the car in decimals or whole numbers? Have you ever heard of anyone telling the speed of his car in decimals? Expect for the last questions I expect all the answers to be correct. Students in fact will enjoy the last question. I will continue with the lesson to explain decimal notation. I will draw a square in the one’s place and call it one whole. The decimal is the “and”, the tenths place is the bars and the hundredths place is the bites (a little square). I will give a square paper to Danvion and ask him to first fold the paper to make 10 bars and then unfold it so that he could see the columns that had appeared due to his activity. At the same time I will demonstrate the activity to my students. When the students will fold the square I will ask him to unfold the paper vertically and count the number of columns that had appeared. He would count the columns and I would place him a question?

• How many columns could you count on the paper?

Once he has given the correct answer, I will then explain him that these columns could also be called bars. For reinforcement I will also demonstrate the activity using paper straws. Once the concept is clear I will instruct them to fold the paper horizontally and count how many small squares they have now. I will draw the grid with hundred small squares on the board.

• How many small squares do you have?

I expect a correct answer from Danvion. I will then explain that ten columns or bars make up one square, 10 small squares make up one bar and 100 small squares make a one big square.

I will draw a whole square, a square with 10 columns and a big square in the right place with 100 small squares inside. I will explain students that columns are also called bars. I will label a whole square as One’s/1, a square with 10 bars as tenths/10 and a big square with 100 small squares inside as hundredths/100. I will begin discussion by encouraging students to participate, ask questions and answer any questions. I will reinforce the concept about the one’s place being whole numbers through continuous practice. This method will also help us when we will take up comparing decimals. I will tell the students to compare one number at a time instead of looking at how the number looks. If one number has one whole and the other does not, the students will be encouraged to think and then answer by comparing the smaller number with the bigger. If the number does not contain any whole number, students will be encouraged to think which number contains the most bars. I hope students like Danvion will distinguish quickly. First it will sound confusing but students can enjoy doing such activities through continuous reinforcement. I will take four weak students. Of course Davison will be one of them. I will make two groups. One group will practice the “th” sound and the other will practice the “s” sound to open the discussion. Suppose if a man is six and a half feet high, how will we write this in decimal numbers? We can write the number 6 as a whole number. For half a feet we use a decimal notation. We will write six and a half as a decimal form as 6.5. This could lead into an interesting discussion. Students can ask a set of questions. For example why 6.5 instead of 6.6. Twelve inches make one foot. Why then 6.5?

Here students will be explained that we are studying whole numbers and the decimal notation, not the measurements. To put a half or a quarter of a number we use a decimal system. To introduce decimals to Danvion using the following method, he need to have had some previous experience of fractions (in particular tenths).

Let’s look at a normal whole number: 345

We can break this number to see how it is constructed. The construction of a number 345 means 3 of 100s + 4 of 10s + 5 of ones.

Now imagine extending the number 345 to show some hidden numbers. These numbers have been taken away because they have no real value at all.

Consider 345 in the place value table. I will explain the students to notice the place value for the position immediately on the right. In other words the place value for each position is 1/10 of the place value for the position immediately on the left. Suppose we place a point or a period called a decimal point after the digit which occupies the unit place that is the digit 5. Then we place a digit say seven after the decimal point and we 345.7. Similarly if we place a 6 after 7, then we would have 345.76.

The following is the place value table for 345.76.

Numbers like 345.76 are said to be written in the decimal form and we may simply refer to them as decimal numbers.

The expanded form for 345.76 is 3 x 100 + 4 x 10 + 5 x 1 + 7 x 1/10 + 6 x 1/100 OR 300 + 40 + 5 + 7/10 + 6/100. Simplifying this we have 345 7/100 OR 34576/100. Thus we see that the decimal 345.76 is the fraction 34576/100. The above discussion suggests that decimals can be converted into fractions. I will reinforce the concept by explaining students that the number of digits after the decimal points are called decimal places. The students will relate their knowledge of place value and will link this knowledge with the addition of decimals. Slow learners would not have enough built-in logic to understand this reasoning intuitively. The fact that this error pattern occurred under these conditions and not on the two previous measures is also indicative of the way students “compartmentalize” their knowledge of decimals. That is, they are prone to using problem solving strategies inflexibly, or in a highly context specific manner (Lesh, Behr, & Post, 1987; Silver, 1986).

Addition of Decimals are easy to add when these are vertically arranged.

Reinforcement will be on the alignment of decimal points. Students will be explained about the importance of alignment. The decimal points are aligned to keep digits having the same place value in the same column. I will do the following two activities with my students.

Making Decimals

Objective: To make students understand about decimals. Materials Used: Paper worksheets and a pair of scissors.

Instructions:

1. Give each student a decimal work sheet and a pair of scissors.
2. Review with them that decimals are a part of a whole by recapitulating the concept using the squares.
3. Instruct them to cut the decimals out of this one whole piece of paper.
4. Let the students cut out the tenths.
5. Ask them how many tenths did they cut.
6. Review the concept with them that 10 tenths make one whole.
7. Instruct the students to cut one of the tenths into 10 equal parts.
8. Explain them how 10 hundredths will make one tenth.
9. Instruct students to use their paper manipulative to make different decimals such as:.24,.35..47,.59 and.78.
10. Encourage students to make their decimals.

The more the students practice, they will come up with more clarity in their concepts. Build a sense of responsibility in students by asking them to save the pieces in an envelope for further use. This is a good teaching aid for special education children.

Decimal Chart

Objective: Understanding decimals. Materials Required: one white paper sheet, one blue paper sheet. A black color pencil, a cloth to blind-fold, a pencil, and a pair of scissors.

Instructions:

1. Fix a sheet of white paper on the bulletin board.
2. Take a colored sheet of paper. Cut it in 9 equal parts and write numbers from 1 to 9 on them.
3. Draw two little circles with a pencil. Cit them out and color it black.
4. Give one small circle to one of the student.
5. Blindfold the student. Now put the second circle somewhere on the paper.
6. Fix four numbers, two wholes and two decimals in one line but at a distance on the white paper.
7. Fix the small black circle after the two whole numbers on the paper.
8. Encourage the student to walk blindfold up to the paper and try to fix the small circle in his hand over the circle fixed on the paper.

Repeat this activity many times. If the students succeed in their effort, praise them and reward them. These activities can be used frequently.

Results

I am well aware of the performance changes that will occur during the lesson for the students. It could include learning what a decimal notation is, learning the alignment of a decimal point, learning about place values in decimals, learning about addition of decimals and solving problems related to addition. With the strategies used to explain decimals and then giving a worksheet at the end, I expect correct answers from my students. This would indicate that they were able to grasp the concept and were then able to transform it into their own words to write the answer. I will not design higher order thinking questions. I will design questions about the key concepts that students need to learn to gain a deeper understanding of decimals. After one day I will present Danvion a worksheet to complete it to judge how well he has understood the decimal system. I do not expect much from Danvion, but if he did recapitulate a little, I would be satisfied by the achievement made by student. Regarding the two activities, I expect students to show a varying degree of performance on making decimals. This will come with more practice. Special education children need prompting from the para educator to remember that they have to make the two circles meet in activity two. In the case of decimals, whole number instruction –which typically precedes the teaching of decimals – there is a major source of the misconceptions (Resnick et al., 1989). To achieve high levels of procedural competence using traditional instructional methods, is the most important or relevant mathematics for special education students. Cawley and Parmar (1990, 1992) argue that protracted drill on math facts and computational procedures does little to prepare students for the kinds of mathematical problem solving that they will need in the world of work.

Discussion

Implications of the result will indicate whether Danvion has responded well to certain concepts of this lesson. This lesson is designed to search for another option of designing as many activities to this technical approach to understand the decimal system. Learning disabilities are commonly found in special education classrooms. The intervention of my students focused on a visual and conceptual introduction to decimals, followed by conceptually-based practice in the addition of decimals.

In addition to using a clear contrast in instructional methods, I will develop a range of measures to know what students did and did not learn about decimals. In this respect, a main intent of this lesson is to document the effects of the two interventions on student learning. Ten lessons from the Addison-Wesley Mathematics (Eicholz, O’Daffer, & Fleenor, 1983) will be used to provide further computational practice and to allow students to solve problems using calculators. Problems from these ten lessons will be used for practice on aligning decimals, the addition and operation.

I found a consistent difference between the students with learning disabilities who participated in this study and the other students. This may have been due to the small sample size of students with learning disabilities in the study or the stage of learning. That is, differences between students with learning disabilities and other students may be apparent as slow learners will adopte a sense of competence in decimals. (Woodward et al., 1997; Woodward & Howard, 1994).

More activity based learning is needed to confirm and extent the patterns of errors. I would also recommend the continued use of structured activities in this kind of lesson, as these methods tend to confirm patterns that are only partially apparent from the paper and pencil measures.

References

Cawley, J., & Parmar, R. (1990). Issues in mathematics curriculum for the handicapped. Academic Therapy, 25, 507-521.

Eicholz, R., O’Daffer, P., & Fleenor, C. (1983). Addison-Wesley mathematics. Menlo Park, CA: Addison-Wesley Publishing Company.

Lesh, R., Behr, M., & Post, T. (1987). Rational number relations and proportions. In C. Janvier (Ed.), Problems of representation in the teaching and learning of mathematics (pp. 41-58). Hillsdale, NJ: LEA.

Woodward, J., & Howard, L. (1994). The misconceptions of youth: Errors and their mathematical meaning. Exceptional Children, 61(2), 126-136.

Resnick, L., Nesher, P., Leonard, F., Magone, M., Omanson, S., & Peled, I. (1989). Conceptual bases of arithmetic errors: The case of decimal fractions. Journal for Research in Mathematics Education., 20(3), 8-27.

Adding decimals

Name:___________________________________ Date:__________________

0.2 0.4 0.6 0.7

+ 0.9 + 0.0 + 0.4 + 0.6

_______ _______ _______ _______

0.3 0.5 0.2 0.3

+ 0.5 + 0.4 + 0.8 + 0.3

________ _______ _______ _______

0.9 0.6 0.3 0.2

+ 0.0 + 0.9 + 0.5 + 0.4

_______ ________ _______ _______

0.1 0.9 0.1 0.9

+ 0.0 + 0.3 + 0.8 + 0.7

_______ ________ _______ _______

Name:___________________________________ Date:__________________

7.4 8.5 9.3 7.6

+ 0.0 + 0.9 + 2.2 + 8.7

_______ ________ _______ _______

3.01 8.54 8.08 4.34

+ 2.32 + 2.87 + 5.29 + 4.26

_______ ________ _______ _______

34.34 13.52 36.21 76.32

+ 12.56 + 22.40 + 45.87 + 23.33

________ _______ _______ _______

1.256 3.487 4.634 6.778

+ 2.901 + 5.034 + 5.424 + 0.665

_______ _______ _______ _______

Name:_____________________________________ Date:________________

For the student:

What is a decimal point?

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When do we align decimals?

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When we ask to put litres of petrol in our cars, do we ask for whole numbers or decimal numbers?

___________________________________________________________________

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What is the place value of a digit 7 in a decimal number 438.74

___________________________________________________________________

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How many small squares are there in one big square?

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