Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots Artifact 1: TinkerPlots Relative Attributes EXPLORATION Statement of Mathematical Exploration: For this exploration I am going to be using TinkerPlots to explore relations between various attributes that focus on the same topic. In this case, the topic is exercise effects and how these effects depend on specific characteristics of an individual. In this exploration, I am identifying how the attributes that surround this topic depend on each other. There will be five situational comparisons that will visually represent how two attributes are related to each other. I will use the TinkerPlots software to create a number of graphs that will show the relationship between two attributes by manipulating the x and y axes. I will explain the findings in each comparison and provide a screen shot of a graph that represents the data in each situation. I will use the tools in TinkerPlots to represent the situational comparisons in various ways. Exploration A) To start off the exploration of discovering connectives between two attributes, I will construct a graph that shows the relationship between an individual’s weight and gender. By clicking the plot button on the command bar a plot will appear. To label the axes, I will click and drag the weight and gender attributes from the list and drop them on top of the axes. From the graph we see that typically, females weigh less than males. Thus we can make a generalization from this visual that on average weight does depend on an individual’s gender. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots B) The next representation will show the dependency between an individual’s gender and weight category. I will change the labels of the x and y axis to create this representation. I will then click counts and show row percentage from the command toolbar. This will display the percentage of each category. From this added specification on the plot we will conclude that 88% of women are considered underweight compared to only 12% of men. This tool provides a specific percentage of the data that is in each category and allows the user to gain more information from the graph. C) Our next exploration of finding connections between two distinct attributes that represent the same topic is comparing an individual’s height and weight. Again, manipulate the x and y axes to represent the next two attributes that we are trying to find a relationship between. By clicking the averages tool a small triangle will appear on the plot. The user may also click to add in an average bar to make the average more visible. From this visual representation we can see that the average height is about 68 inches. As we compare the weight of these people to their height, we can conclude that they also are of average height. This shows a strong correlation between these two attributes. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots D) The next two visual representations we will analyze together to come up with an overall generalization of the relation between the attributes. The first plot will show the relationship between an individual’s weight category and their pulse rate before they exercise. The second plot will show the relationship between an individual’s weight category and their pulse rate after they exercise. By clicking the drop down arrow on the bottom left of the plot, a list will appear with options of different graphs to choose. In the first graph we used a vertical value bar to show that relationship between the weight category an individual is classified in and their pulse rate before they exercise. In the second graph we used a vertical value bar again but used the stacking tool to represent the relationship between an individual’s weight category and their pulse rate after they exercise differently. The user can find the stacking tool by clicking the icon that has three circles stacked vertically on the top toolbar. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots We can see that an individual’s of a normal weight is able to get their pulse up to a faster pulse more quickly compared to an individual who is overweight. We can see that the number of individuals with a normal weight, exercise much more because there is a much larger representation of them in both graphs. After using the TinkerPlots software as a tool for this exploration we are able to find the relationships between two attributes that focus on the same topic in a useful and visual way. By manipulating the axes of the plots, we were able to conclude different information from each representation. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots Lesson Plan Template: Title: A cooperative learning lesson on data and statistics that incorporates the use of the TinkerPlots software. Subject Area: Mathematics: Data and Statistics Grade Level: 9-12 Concept/Topic to teach: Students will use exploratory data analysis to find the relation between two attributes that focus on the same topic. Students will be assigned in groups of three and will have a role that they will be responsible to fill. Standards addressed: Copy and paste from common core/NCDPI Common Core state mathematics standards o Summarize, represent and interpret data on two categorical and quantitative variables. 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Common Core state standards of mathematics practices o Make sense of problems and persevere in solving them. o Construct viable arguments and critique the reasoning of others. o Use appropriate tools strategically. Technology Standard o Use technology and other resources for assigned tasks. General Goal: Students will engage in exploratory data analysis to develop the skill of generalization and understand the importance of cooperative learning and how to fulfill their assigned role in their small group. Specific Objectives: Content objective: Students will be able to manipulate the axes of a scatter plot using the TinkerPlots software and find the connective information between the two attributes. Pedagogy objective: Students will work together to complete the task by completing their responsibility as a member of the group and report their findings to the members of their group. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots Technology objective: Students will use technology to more easily explore the graphical representations of the data. The software allows students to quickly construct a representation and provides useful tools to find calculations easily. 21st Century skill (Communication, collaboration, creativity, critical thinking): Students will communicate with their group members when they assign different responsibilities and understand what they are accountable for. Students will use critical thinking in the beginning of the class period as they construct their predictions. They will use critical thinking and their background knowledge to develop the representations. In this lesson students will use creative thinking to create scenarios that may fit the graphical representations. Required Materials: Computer lab with available computers for each student (computers must have the full version of TinkerPlots downloaded on it). Anticipatory Set (Lead in): Ask Students open ended questions about the data to set up the exploration 1. What do you notice about the relationship between gender and weight? How can you manipulate a scatter plot to represent this? 2. What attributes does the gender attribute relate to? What observations can you make? 3. Develop an understanding about the rate of pulse for different weight categories. Can you make any assumptions about the health of some of the individuals represented? Step by Step Materials: Before: Grouping and assignment 1. Group students together: in groups of three 2. Assign Member roles: recorder, discussion director, and presenter 3. Discuss Group Norms: a. Recorder: create a document of the findings of your exploration b. Discussion director: instigate group discussion to continue the group’s engagement in the exploration Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots c. Presenter: be able to explain your group’s findings and explain them to your peers 4. Assign tasks and materials to groups a. You will have computers and the TinkerPlot software b. Explore the “exercise effect” data and find answers to the open ended questions. Create graphical representations that show the relation between two attributes. During: What students will be doing: working together with the students in their groups to complete the task. Focus on your role in the group as well as contribute to the main exploration at hand. What teacher will be doing: walk around the classroom to observe which students are on task After: What students will be doing: Move back to your seats and wait for the teacher to close the lesson. What teacher will be doing: evaluate how the students worked within their groups and if they gained a full understanding of the concept. Closure: After working in these small groups we have seen that it helps to share responsibilities with other students. As a team we have different ideas working together and will be able to create a well-rounded exploration of this data. Assessment Based on Objectives: Include Rubric you will use to grade student work Adaptations If there are students that do not have the prior knowledge to be able to create predictions about the data, I will ask their group members to explain what they need to know. This will allow for more communication and enhance the connection between group members. Extensions Give students a new set of data and ask them to complete the same task within their small group but ask them to develop their own questions to explore. Instruct the students to create one list per group of open ended questions and as they manipulate the axes of the graphs, explore for the answers to their questions. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots INSTRUCTIONAL DESIGN PLAN (IDP) INSTRUCTIONAL DESIGN Plan for Lesson NAME: Danielle Hartquist Instructional Design Plan Content. Data and Statistics Select content from the Common Core for Mathematics go to page 79 Pedagogy. Pedagogy includes both what the teacher does and what the student does. It includes where, what, and how learning takes place. It is about what works best for a particular content with the needs of the learner. Include 21st Century thinking skills: creative, critical, innovative, problem solving www.p21.org You may focus on just critical, or just creative, or both critical thinking and innovative problem solving. See: Creativity and Innovation Critical Thinking and Problem Solving DATE:10/12/12 Describe content here. Select from only 1 competency or standard. Core competency: Summarize, represent, and interpret data on two categorical and quantitative variables. 6. Represent data on two quantitative variables on a scatter plot, and describe how the variables are related. Concept, principle, process, methodology: Students will have two distinct variables and use the graphical representation of their relation to create generalizations about the topic and understand the concept of dependence between two attributes. Students will be assigned a certain role in their small group and will be able to fulfill the responsibilities they were assigned. 1. Describe instructional strategy (method) appropriate for the content, the learning environment, and your students. This is what the teacher will plan and implement. The class will be held in a computer lab where each student has their own computer to work on. The students are already familiar with the TinkerPlots software so the teacher will instruct them to get the software open on their computer. The teacher will instruct the students to use TinkerPlots to create graphical representations of their predictions of what they think the relations between the attributes we looked at in the exploration, will look like. The teacher will ask the students to take screenshots of their predictions and keep them in a document. The teacher will provide the students with the “exercise effects” data in TinkerPlots and allow them to explore it and create new representations using the data provided. The teacher will assign students into small groups of three students and give them open ended questions to explore while working with their small group. Each student will be assigned a specific role in the group. The three roles are recorder, discussion director, presenter. The teacher will explain that all of the students are responsible to Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots work together on the exploration of the data. The recorder is responsible for creating the final product to turn in for the group. It’s the discussion director’s job to ask their group members questions to keep the exploration going. It is the presenter’s job to present their group’s findings to the rest of the class. The teacher will evaluate the success of each group by assessing if each member met the responsibilities of their role. 2. Describe what learner will be able to do, say, write, calculate, or solve as the learning objective. This is what the student does. The students will work with the TinkerPlot software and explore the relation between two attributes. They will be able to explain what a graphical representation shows. The students will work together in small groups and understand that they each have a personal role in the group. The students will create a final product that outlines their findings and they will be able to explain their findings to their peers. 3. Describe how creative thinking--or, critical thinking, --or innovative problem solving is reflected in the content. Students will use critical thinking in the beginning of the class period as they construct their predictions. They will use critical thinking and their background knowledge to develop the representations. In this lesson students will use creative thinking to create scenarios that may fit the graphical representation. Technology. Digital tools using computers, Internet, and related technologies. Reflect—how did your lesson activity fit the content? How did the Describe how the technology enhances the lesson, transforms content, and/or supports pedagogy. Describe how the technology affects student’s thinking processes. The students will be using a computer and the TinkerPlots software in this lesson. TinkerPlots gives the students a visual representation to easily compare the relation between two attributes. They are able to construct graphs and analyze the relation between the attributes that are represented on the axes in a timely manner. Thus, this software gives the students more time to come up with generalizations about the topic and to determine the relationship between the attributes. Reflection should be written here: Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots technology enhance both the content and the lesson activity? TinkerPlots is an extremely useful software that allowed the students to work through This exploration in a different way. Using the software for this exploration made the class Period more hands on and exciting for the students. The software helped to illustrate what Each graph and relationship between the attributes looked like. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots Rubric 1 2 3 Contribution to group goals Works toward group goals only when prompted Works toward group goals with occasional prompting Works toward group goals without occasional prompting; accepts and fulfills individual role within group Completion of Individual Role Works toward individual role only when prompted Works toward individual role with occasional prompting Works toward individual role without occasional prompting; accepts and fulfills individual role within group Contribution of knowledge Contributes information to the group only when prompted Contributes information to the group with occasional prompting or reminding Contributes knowledge, opinions, and skills without prompting or reminding Success of Exploration Group goals are not adequately met Group goals are starting to develop but are not quite adequate. Group goals are proficient, effort is shown. 4 Consistently and actively works toward group goals; willingly accepts and fulfills individual role within group Consistently and actively works toward individual role; willingly accepts and fulfills individual role within group Consistently and actively contributes knowledge, opinions, and skills without prompting or reminding Group goals are fulfilled, effort was fully demonstrated. Danielle Hartquist Mate 4001 Data and Statistical Artifact: TinkerPlots REFLECTION The TinkerPlots software is an easy-to-learn and use software that allows the user create a visual representations of the data they are exploring. The software has multiple tools that show the mean, median and mode of a set of data, instantly. TinkerPlots also includes the separate, order and stack tools to organize the data in the plot to make it more legible for the user. In this particular exploration, it was beneficial to be able to separate the data into different sections in the plot and turn on the percentage tool. This allowed the user to analyze the plots in a timely manner and have correct information from the data plots to work with. TinkerPlots is dynamic software. The user was able to manipulate the axes of the graphs to help them develop a relationship between the two attributes that were being represented. For example in this case, how heavy an individual is depends on how tall they are. This tool made it easy to see this dependence because of the location of each point on the plot. TinkerPlots also allowed the user to create different types of graphs that made the data easier to evaluate. In this exploration, once the user denoted which attributes they wanted to represent the x and y axis, they could change the type of graph by the click of a button and decide which type of graph best represents that data comparison. TinkerPlots software separates clusters of data and uses color classification to assist the user in analyzing the data they are working with. All in all the TinkerPlots software provided a beneficial visual aid for this exploration. This technology tool will help students to understand this data exploration and the concept behind the lesson. As described above, TinkerPlots provides a beneficial visual aid for the user which makes the task easier to complete. The software shows the user what the data looks like on a graph and provides tools that highlight the specifics in the data set. This tool will enhance student understanding.