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Chapter 4 week 4 Notes

by: Morrissette32

Chapter 4 week 4 Notes Sped 482

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notes for chapter 4
Direct instruction in Mathematics
Mrs. Mohney
Class Notes
direct instruction, Math, sped482
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This 4 page Class Notes was uploaded by Morrissette32 on Monday February 15, 2016. The Class Notes belongs to Sped 482 at Clarion University of Pennsylvania taught by Mrs. Mohney in Spring 2016. Since its upload, it has received 21 views. For similar materials see Direct instruction in Mathematics in Special Education at Clarion University of Pennsylvania.


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Date Created: 02/15/16
Chapter 4: Counting Difference between rote counting and rational counting Rote counting- Identifying number names in sequence. st 1ndrade- count to 99 2rdrade-count to 999 3 grade- count into thousands Prerequisite for rational counting Rational counting – Identifying the cardinal number of a set, i.e. object counting; sometimes called one-to-one correspondence. Coordinating counting with the touching of objects to determine the quantity of a particular set. In order to determine the content of the initial rote counting exercises Teachers will ask students individually to count as high as they can and the performance of the group determines which new numbers are introduced. five steps in the format for Introducing New Numbers. 1. Teacher tests students on previously introduced numbers (1-10) 2. Models counting (1-13), then models just the new part (11, 12, 13) 3. Teacher leads students in saying the new part (emphasizing the new numbers by saying them in a loud voice) 4. Teacher tests them 5. Teacher has them say the entire counting series from 1 through the new part. (delay test) rate the teacher should expect students to count in the first rote counting tasks One number per second, then 2 numbers each second (at a lively pace). Rate is important because …Helps keep students attentive and facilitates learning the number sequence. Rational Counting format Teachers initially use pictures to teach rational counting. Part A – Teacher touches lines as students count and then asks what number they ended with. The teacher must then use clear signals when touching the lines. Part B- the students count illustrations of objects on their worksheets. Part B objects in the illustrations should be placed at a half an inch from each other. They touch each object when they hear the teacher clap (1-1.2 second intervals) Monitoring students with rational counting When the skill is first taught the teacher must repeat the task until he has watched each student touch some objects as the student counts. Monitoring at the very start of the task is also important. If students do not begin at the first picture, they will make mistakes. Note: counting can be done from left to right or from right to left. However, to facilitate monitoring the students should always count from left to right. errors students are likely to make when counting two groups of lines The error students are likely to make in Part A occurs when they are asked to count all of the lines. After counting the lines in the first group, a student is likely to say “one” for the first line of the second group instead of continuing to count. To correct, the teacher models and tests students on that step, and then repeats from step 2. Example: “When we count all of the lines, we keep on counting. My turn: 1,2, 3, 4, 5, 6.” The teacher then tests the students on counting all of the lines and then repeats the steps that are linked. Students count the lines in the first group, then the lines in the second group, and finally count all the lines providing a delayed test for the original task on which the error occurred. Reasons to start counting from a number other than one 1. Saves time when teaching rote counting to higher numbers. If students can start at numbers other than 1, teachers can focus on the relevant parts of number sequences. 2. This counting skill is a component of the early addition strategy. preskills related to counting beyond 30 1. rote counting beginning at a number other than 1 2. skip counting by tens the procedure for teaching how to count to 50 if the student can already count to 40 First the new part begins at a tens number ending in 7 and continues through the next tens number ending in 2. Instead of testing students on counting from 1, the teacher has them count from a number approximately 10 to 20 numbers lower than the new part. After students practice counting though a new decade for 2 days, the examples are modified daily to promote generalizability. Example: students might count from 27 to 42 one day, from 25 to 47 the next, and from 27 to 49 the next. three stages in teaching to count in the hundreds. Stage 1-The teacher has students count a single decade within a single hundred (ex. 350- 359). The teacher uses a model-lead-test procedure on four to five sets of examples each day. Stage 2-The objective is making the transition from one decade to the next (ex. 325-335). An example set should include several series extending from a number with 5 in the ones column to the next number in the counting series that has a 5 in the ones column. Stage 3- Focuses on the transition from a hundreds series to the next hundreds series (ex. 495-505). This example set should include several series extending from a hundreds number ending with 95 to the next number in the counting series that has a 5 in the ones column. Skip counting series Knowledge of the count-by-series for multiples of 2,3,4,5,6,7,8,9, and 10 is an important component skill for the memorization of basic multiplication and division facts. Students should learn to count 10 numbers for each series (except fives): 2 to 20, 3 to 30, 4 to 40, 6 to 60, and so on. Students should learn to count by fives to 60 since telling time requires this skill. Teachers also may want to teach counting by twenty-fives to 100 as a prerequisite to counting money. Students are fluent on a specific series when they can say the series within approximately 8 seconds. Suggest teaching count-by series cumulatively in the following sequence: 10, 2, 5, 9, 4, 25, 3, 8, 7, 6. Separating similar series helps prevent errors in which students switch series. The count by format includes two parts. Part A demonstrates to students that they end up with the same number whether they count by ones or count by another number. Also, the demonstration is intended to show that counting by a number other than 1 can save time. Part A would be presented just for the first lessons in which count by twos and fives are taught. Part B is designed to teach students to memorize the various count by series. Part B of the count by format also includes a review of previously introduced count by series. Two or three previously taught series should be reviewed daily. The teacher uses a model-lead-test procedure, saying the numbers of the new series alone, saying the numbers of the new series with the students and finally having the students say the numbers themselves. Naïve students introduce just the first three numbers of the series More sophisticated students might introduce five or six numbers. On the second day of instruction on a series, the teacher tests the students on the part of the series taught during the previous lesson. If the students make an error, the teacher repeats the model lead test procedure from steps 2 and 3 of Part B. If the students know the part of the series previously taught or require just a couple of practice trials to say the previously taught part correctly, the teacher introduces the next several numbers of the count by series. The new part includes the last two familiar numbers and the next two or three numbers in


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