Thomas Allen11/5/13MATE 4001Dr. Adu-Gyamfi

Artifact 1: Exploring the statistics of Soccer’s World Cup using Fathom Scatterplots and Box Plots

Statement of Mathematical Exploration:

Throughout this exploration I used the Fathom software to compare relationships of different aspects of soccer such as wins, losses, games played, and points scored for and against that team etc.. I firstly created an assortment of scatterplots that may determine whether there exists a correlation between 3 sets of data. Secondly, I proposed questions relating to the various scatterplots to determine what conclusions if any could be stated given the sets of data.

Above is the given information relating to countries and their statistics.

1) What can be said about the number of wins a team achieved and their respective points scored for and against that team?

It is obvious that the number of wins a team accrued increased as the number of points a team scored for their team was greater than the points scored against them.

2) What characteristics of this scatterplot helped you to draw this conclusion?

It is clear that the blue dots represent the points scored against a team and the gray representing the points scored for that team. It is present in the graph that the teams who have gray dots above that teams blue dots. If this relationship is reversed then that team had a losing record.

3) There seems to be a gradual increase in the difference between number of points that team scored for themselves and the points that were scored against them that varies directly with the number of wins that team accrued, why is this?

It shows that the teams who were consistently successful in winning games their ratio of points scored for their team to points scored against them were larger than those with fewer wins. Showing a direct relationship between the number of wins earned and increasing ratio of gray:blue dots.

1) What is the range of points scored against the teams, what does this reveal in regards to the variance?

The range is from 3 to 103, the plot illustrates a large variation due to the span of the fourth quartile and value of the outlier.

2) Does the outlier of the graph have an effect on the median or the mean? Explain why box plots use the median instead of mean?

It has an effect on the mean of the entries; because the mean is the average of the sum of the entries of the data set causing it to be susceptible to a large outlier causing the graphs information to be skewed or untrue. Whereas a median splits the data into two sets illustrating that doesn’t deviate unless large amounts of entries are added to the data set.

3) What are the pros of using this type of graph help organize and present the large data set?

The plot allows the observer to quickly organize large sets of data into four compact sets of data. The plot allows you to find the value of a median that isn’t affected by outliers of large or small value.

1) How do you suppose the histogram can provide potential insight into the given data set? Explain.The histogram displays the range of pts the teams received and groups the teams within 10 pt intervals. The histogram explicitly shows how many teams accumulated the amount of pts and grouped them within their respective 10 pt interval located on the x-axis. This histogram provides insight to which teams will potentially perform the best.

2) How can this histogram help evaluate a team’s efficiency? Explain.

Yes, It clearly separates the teams by their success on the field by distributing the teams according to the number of points they have gained by winning, tying and losing matches and as well as explicitly showing the frequency of teams with similar success.

3) What do you suppose the relationship between the standard deviation, mean and outliers is? ExplainThe mean is the average of in this case cumulative points earned or the “central tendency” and the standard deviation measures the spread of elements of the data set around the mean. Since the standard deviation is a measure of the mean and the mean is affected by extreme large or small values the standard deviation becomes an insight to the presence of outliers and loses or makes it difficult to accurately quantify the spread of the data set.

IDP TPACK TEMPLATE (INSTRUCTIONAL DESIGN PROJECT TEMPLATE)

NAME: __Thomas Allen__________ DATE:_____11/5/13___________

Content. Describe: CCSS.Math.Content.HSS-ID.B.6 Represent data on two quantitative

variables on a scatter plot, and describe how the variables are related.

Describe: Standards of mathematical Practice Make sense of problems and persevere in solving them. (derive

meaning of a problem) Reason abstractly and quantitatively. (reason and construct viable

arguments) Construct variable arguments and critique the reasoning of others. Model with mathematics. (mathematical structure) Use appropriate tools strategically. (derive meaning of a problem

and/or mathematical structure) Look for and make use of structure. (reason and construct viable

arguments) Look for and express regularity in repeated reasoning.

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.

1. Describe instructional strategy (method) appropriate for the content, the learning environment, and students. This is what the teacher will plan and implement.

Teacher will give students the scatterplots and the respective questions for the students to study and critically think and draw conclusions using inferential statistics.

2. Describe what learner will be able to do, say, write, calculate, or solve as the learning objective. This is what the student does.

Students will be able to accurately create scatterplots boxplots and Students will work in groups of three to communicate ideas and

facilitate the learning objective and concepts. Students will come to a unanimous conclusion that all three agree

states what they believe each scatterplot illustrates using correct logic.

3. Describe how creative thinking--or, critical thinking, --or innovative problem solving is reflected in the content.

Students will be compelled to use prior knowledge of various graphs and plots to help them critically think and make well educated inferences about large data sets.

Students will have to contemplate the logic behind each graph or plot they create to represent their correlations thereby being required to explain their logical conclusions and defend.

Technology.

1. Describe the technologyFathom helps organize and construct a multitude of plots using complex sets of data.

It allows users to plot information in various ways that may infer a correlation or causation relationship between the two or three sets of data.

2. Describe how the technology enhances the lesson, transforms content, and/or supports pedagogy.

The technology enhances the lesson by making it faster to graph and plot the data.It also makes it easier to isolate specific sections of the sets of data allowing users to further breakdown large scale sets of information.

3. Describe how the technology affects student’s thinking processes. The technology helps students make correlations quicker and allows

them to make inferences about the data that may have otherwise been too problematic or complex.

Reflect—how did the lesson activity fit the content? How did the technology enhance both the content and the lesson activity?

Reflection

Title: Using scatterplots to analyze statistics and make inferences.Subject: Mathematics Grades: 9-12Concepts: Analyzing statistical information and drawing appropriate conclusions.Standards addressed:

Common core state mathematics standards CCSS.Math.Content.HSS-ID.B.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

Make sense of problems and persevere in solving them. (derive meaning of a problem)

Reason abstractly and quantitatively. (reason and construct viable arguments)

Construct variable arguments and critique the reasoning of others.

Model with mathematics. (mathematical structure)

Use appropriate tools strategically. (derive meaning of a problem and/or mathematical structure)

Look for and make use of structure. (reason and construct viable arguments)

Look for and express regularity in repeated reasoning.

Technology standards Sources of Information

o Evaluate resources needed to solve a given problem

HS.S.1 - Evaluate resources for reliability. (Reliability can be determined by currency, credibility, authority, etc. depending on the curriculum topic).

HS.SI.1.2 - Evaluate resources for point of view, bias, values, or intent of information.

HS.SI.1.3 - Evaluate content for relevance to the assigned task.

General Goal:Students will analyze each scatterplot and draw conclusions according to each question specified.

Content objective:

Students will become more efficient at using inferential statistics to draw logical conclusions and make educated responses in regards to scatterplots and the relationships they can depict.

Pedagogy objective:

Students will collaborate educated ideas and assumptions to reach plausible conclusions based of the evidence given using fathom produced scatterplots.

21st Century skill (communication, collaboration, and critical thinking):

Students will communicate and collaborate with one another and use each other to gain a deeper insight into the concept of using technology such as fathom to create organized visual representations of difficult sets of data.

Required Materials:

Computer

Fathom software

Notebook and pencil

Questions students will answer during exploration:

1) What can be said about the number of wins a team achieved and their respective points scored for and against that team?

2) What characteristics of this scatterplot helped you to draw this conclusion?3) There seems to be a gradual increase in the difference between number of points that team scored for

themselves and the points that were scored against them that varies directly with the number of wins that team accrued, why is this?

4) Is there a positive correlation between the number of games played (P) and the number of wins a team accumulated? Explain.

5) Is there a correlation between the number of games played (P) and the number of losses a team accumulated? Explain.

6) What other relationships can you interpret from the given scatterplot? Explain. 7) How do you suppose this scatterplot can be misleading? Explain.8) How can this scatterplot help evaluate a team’s efficiency? Explain. 9) Does the information and the form that it is given help determine which teams have a more positive

likelihood of succeeding in upcoming World cup tournaments? Explain.

Four phase plan

Phase 1: Problem Posing

Students will be given a set of data in regards to the world cup and each countries statistics. Students will be asked by their instructor to construct a visual representation that appropriately distinguishes variations or relationships within the given data set using fathom. Which they will in the end of the period present as a group their findings.

Teacher will be:

Giving the instructions

Introducing the problem and expectations

Grouping students into groups of 3

Students will be:

Writing down what is expected

Communicating with their group peers about how they should meet the requirements.

Phase 2: Small group instruction

Students will be directed to fathom and given the problem and the instructions through means of a worksheet. Students will illustrate their answers as well as give an explanation within fathom. Each student will be responsible for contributing equally to the groups findings.

Teachers will be:

Circulating the room and asking probing questions to get the students to think more critically about the assignment

Students will be:

Working together in their groups and collaboratively creating their unique solution to the problem posed.

Phase 3: Whole class discussion

The class as a whole will evaluate each groups representation and ask educated problems as well as give constructive criticism on how might they can make improvements if any can be.

Teacher will be:

Evaluating each groups findings and how well they defend their answers using concepts and skills learned.

Writing notes on how each groups presentation of their findings can be improved as well how much effort they put forth to completing the assignment and meeting his/hers expectations.

Students will be:

As a group presenting and defending their method or approach as well as their findings using appropriate mathematical vocabulary and logic.

After presenting sending their findings they found using fathom to thei instructor for further evaluation.

Phase 4: Summarizing and Extending

The teacher will review each group’s work they submitted and ask further questions for the students to think about and make changes were they as a group agree should be made to make their methods and findings more accurate.

Teacher will be:

Reviewing over groups submitted presentations and correcting as well as asking questions that may require students to think about the problem more critically.

Students will be:

Revising their presentations if necessary as a group and resubmitting their refined presentations.