Understanding K–6 Statistics: Standards and Lesson Examples

Kyle Clinedinst Student ID-001029234 BMM2- Task 3: Understanding and Teaching Statistics, Data Analysis, or Probability Part A: A. Study the statistics, data analysis, or probability content standards for your state and do the following: 1. List three content standards from your state that apply to statistics, data analysis, or probability for grades K–6. The three selected standards must represent three different grade levels. Grade 1: “ 1.MD.4 Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another.” -Ohio Learning Standards/Mathematics Grade 1 Grade 2: “2.MD.10 Organize, represent, and interpret data with up to four categories; complete picture graphs when single -unit scales are provided; complete bar graphs when single -unit scales are provided; solve simple put -together, take -apart, and compare problems in a graph.” -Ohio Learning Standards/Mathematics Grade 2 Grade 3: “3.MD.3 Create scaled picture graphs to represent a data set with several categories. Create scaled bar graphs to represent a data set with several categories. Solve two-step “how many more” and “how many less” problems using information presented in the scaled graphs. For example, create a bar graph in which each square in the bar graph might represent 5 pets, then determine how many more/less in two given categories.” -Ohio Learning Standards/Mathematics Grade 3

2. Write a sample problem for each of the three standards to illustrate the evolution of student understanding. Grade 1:

Grade 2:

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Grade 3:

3. Provide a solution for each problem that demonstrates each step or explains the thinking process involved in determining the solution. Grade1: Thinking- For this problem, students start to learn how to organize data. They are given data that is scrambled, and they must count the number of basketballs, baseball, and

soccer balls. They learn that data can be represented in a number of ways and data can be used to answer questions. Grade 2: Thinking- For this problem, students learn that symbols and pictures can be used to represent data. In this simple picture graph, students need to first find the number of students that voted for each subject by counting the number of stars. Then, they will

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find the number of students who voted for math (7) and reading (3). Next, they need to know the operation by understanding “how many more” and “than” means to subtract. Finally, they will subtract 7-3=4. Grade 3: Thinking- For this problem, students must make a picture graph by using the data in the frequency table. To do this, they first need to find the scale/key. They will need to notice that each number in the table is a multiple of 5. Next, students will make the picture graph by using multiples of 5. For the question, students will need to know that it has 2 parts. For the first part, students will add the number of dogs and cats. 35+15=50. Next, they will subtract that

number by the number of fish to find how many more students like dogs and cats combined than fish. 50-25=25 4. Discuss how the chosen standards and problems build student understanding of statistics, data analysis, or probability across the three K–6 grade levels selected in part A1. The first reason I chose these standards is because I have not done a lesson plan for 1st grade and I wanted to see how these standards align from the younger grades to the older grades. More importantly, I chose these standards to show how data analysis progresses from 1st grade to 3rd grade. I find that many incoming third graders really struggle with multi- step word problems dealing with data analysis. I wanted to see how the standards align. In 1st grade, students start to learn what data is and means. They learn to organize data in a variety of ways. Then, in 2nd grade, students start to create and read simple graphs and charts with a scale of 1 as shown in my problem above. They are also asked to solve 1 step word problems related to the graphs. I feel like the standards in Ohio take a big jump from 2nd grade to 3rd grade. In 3rd grade, students now need to create and read graphs with larger scales. They also need to solve multi- step word problems related to the data. If students struggle with reading graphs with larger scales, they have no chance to answer multi-step word problems related to the graphs. Part B: Watch the “Graphing with Colors” video and do the following: 1. Discuss why you think the teacher chose to have students gather squares and what impact this had on the beginning and end of the lesson. I think the teacher had the students gather squares because it gets students moving, interested in the lesson, and in charge of their own data. The first thing this lesson has is students moving around the classroom. Students learn better by being active and involved. Also, the students obviously liked looking for the squares. They are excited to learn. Another aspect of having the students look for squares is that the students are in charge of gathering their own data. If a teacher just gives the students data, it’s not nearly as effective. Also, each group has different data so there are many different strategies and ideas being discussed in the classroom. At the end of the lesson, students relate the squares and data to other academic areas. When the teacher asked why it was harder to find the clear squares, one boy said, “a clear one can be an animal that is camouflaged.” Another student whispers “like an iguana.” This imbeds science vocabulary into a math assignment.

2. Discuss the advantages and disadvantages of teaching this lesson in small groups versus having students work individually. There are many advantages to teaching this lesson in a small group. First, students learn better from their peers. As described by Van De Wallie & Karp & Bay-Williams, 2012, p.99, students with special needs (and all students) benefit from others’ modeling and support, including modeling by their classmates or peers. Next, students enjoy working together. This is another way to get students interested in the lesson. Finally, it allowed for the students to have more data. If they were to work individually, some students would have very little data because they didn’t find many squares. The only disadvantage I can think of is that working in small groups makes it harder to assess individual knowledge. It is hard for the teacher to give a summative assessment in small group situations because often the students who are on level or above take lead of the group. This is great for below level students to learn from their peers but makes it hard to assess their individual level. 3. Describe one specific modification you would make if you were teaching this lesson and explain how the modification would deepen understanding of statistics, data analysis, or probability. A modification I would make to this lesson would be to have the students write their own word problems based on their data. For example, “How many more green squares are there than clear squares.” A 3rd standard is to analyze data and answer questions involving all 4 operations. Well, if we teach students to write questions based on data, then that’s higher thinking. And if students can write reasonable questions, they definitely understand and can answer word problems dealing with data analysis. Part C: Prepare to create an original lesson plan on statistics, data analysis, or probability by doing the following: 1. Describe an evidence-based instructional strategy that will be incorporated into your original lesson plan. For this data analysis 1st grade lesson, I will have students create and analyze tables in small groups as peer-assisted learning. For this lesson on collecting and analyzing data, I will have students pull marbles out of a bag and use that as our class data. They will work in small groups to organize their data by making a table using tally marks and

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numbers. The students will be in groups of 3-4, with students at all different levels in each group. a. Explain why the chosen instructional strategy would be beneficial in a lesson on statistics, data analysis, or probability using evidence from a credible source to support your selection. I chose this strategy because “students with special needs benefit from others’ modeling and support, including modeling by their classmates or peers.” -( Van De Wallie & Karp & Bay-Williams, 2012, p.99) When making small groups, I’ll be sure to have students who are above or on level in terms of analyzing data work with those who are below level. This will help support the students with special needs or those who struggle with data analysis. “The students can be paired with older students or peers who have more sophisticated understandings of a concept.” -( Van De Wallie & Karp & Bay- Williams, 2012, p.99) Part E: Ohio Learning Standards Mathematics . (2017). Ohio Department of Education. https://education.ohio.gov/getattachment/Topics/Learning-in-Ohio/Mathematics/ Ohio-s-Learning-Standards-in-Mathematics/MATH-Standards-2017.pdf.aspx? lang=en-US Bay-Williams, J.V.D.W.K.S.K.J. M. (2012). Elementary and Middle School Mathematics: Teaching Developmentally, VitalSource for Western Governors

University (8th Edition). Pearson Learning Solutions. https://wgu.vitalsource.com/books/9781256957669

Task 3

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