Jimmy Clemson

Dr. Adu-Gyamfi

MATE 4001

11/3/13

Artifact 1

Every summer I go to amusement parks to ride rollercoasters. I try to get to new places

all the time to experience new rides but each time I go to a new amusement park I never know

which coaster to go to first. I need to find some way to narrow down the options a little so the

decision becomes a little bit easier. So should I go to a wooden coaster or a steel coaster first?

Question: What are the statistically significant differences between wood roller coasters

and steel roller coasters? Take p<.05 to determine significance.

To start looking at this question I first took the category of largest drop. I created a graph that

displayed the largest drops of steel tracks versus wooden tracks. While the steel tracks have

higher values, it also has much more variability. The mean of the steel is 193.5 while the wood

was 132.7. The test statistic is 1.398. The probability for a test statistic of t=1.398 is .19.

Since .19>.05 this is not a statistically significant difference between the two populations. Even

when only looking that μsteel>μwood yields a p value of .09 which is still not a significant result.

From there I went to test the differences in the heights of the coasters. The story of this category

is much the same as the last one. The steel coasters have a higher mean and much more

variability than the wooden coasters. The means are, steel=194.125, wood=132.571. The

standard deviations are steel=105.292 and wood=51.7232. With a t value of 1.464 and a

corresponding p value of .17, this is also not a statistically significant difference between the

wood and the steel coasters. Next I will test the length.

Looking at the length of the coasters now, we can see that the means of the two distributions are

very similar with the steel coasters once again having the most variability. The means and

standard deviations are as follows: mean of steel is 4527.62, mean of wooden is 4380, standard

deviation of steel is 2333.97, standard deviation of wood is 1565.02. With a t value of 0.1454

these two distributions are extremely similar. This corresponds to a p value of .89 which is

definitely not statistically significant. So far I have not found one category that is statistically

significant between steel and wooden coasters. Next I will look at top speed.

Here we have two distributions where the steel is more varied than the wooden coasters and also

has a higher mean than the wooden. In this one there is one particular outlier that is really

skewing the steel data. The means and standard deviations are as follows, mean for steel is 69

and for the wood is 59.9, the standard deviation for the steel is 27.7 and for the wood is 12.58.

The test statistic is .831 which corresponds to a p value of .43. Now we have looked through

each of the attributes and there are not any that are statistically significant. I wonder if the

outlier in this last case is skewing the data too far, so I am going to see if that is the case.

After having deleted the outlier which was named Cobra and was a family ride which seemed to

be skewing the data, we have some new information. The mean and standard deviation of the

wooden tracks are the same but the standard deviation and mean for the steel tracks are slightly

different now. The mean is now 76.2857 and the standard deviation is now 20.0559. With these

new measures we now have a test statistic of 1.826 which corresponds to a p value of .097. By

taking out the one outlier we have shown there is more of a difference in their distributions than

thought was there with the outlier even though this still doesn’t qualify as statistically significant

if we use the defined significance above.

IDP TPACK TEMPLATE (INSTRUCTIONAL DESIGN PROJECT TEMPLATE)

NAME: ______Jimmy Clemson______ DATE:________11/4/13________

Content. Describe: content here. (COMMON CORE STANDARDS)

CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized

experiment to compare two treatments; use simulations to decide

if differences between parameters are significant.

Describe: Standards of mathematical Practice

CCSS.Math.Practice.MP1 Make sense of problems and persevere

in solving them.

CCSS.Math.Practice.MP2 Reason abstractly and quantitatively.

CCSS.Math.Practice.MP3 Construct viable arguments and

critique the reasoning of others.

CCSS.Math.Practice.MP5 Use appropriate tools strategically.

CCSS.Math.Practice.MP6 Attend to precision.

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.

This will be an exploratory lesson. The students will already have learned what hypothesis testing is and have been introduced to a two sample t-test. I will review this at the beginning of the period and then introduce the data. From here I would ask the students about different roller coasters they have been on and their experiences on them. After each response I will try to find out what kind of coaster it was and then pose the question are there any significant differences between the wooden and steel coasters.

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

From there the student will explore whether there are any significant differences between the two. They will soon find out that there are no statistically significant differences.

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

For the most part what the students have done so far will not have involved too much critical thinking. They so far have just had to know how to do a significance test and understand what each of the values produced means in context.

Once the students see that none of the ones are significant, I will prompt them to think about why that is even though there seems to be quite a discrepancy between the distributions. I will have the students write up why they think it is that there wasn’t any significant difference and have them turn it in.

Technology.

1. Describe the technology

The technology used was Fathom. Fathom is a micro world technology that focuses in the use of statistics. It allows easy use of graphs and tests involved in inferential statistics.

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

The technology allows the students to see a graph of each of the categories with wood versus steel. By seeing this they can see that there is discrepancies between the two distributions and it is reasonable to test if they are different or not. By doing the significance tests on fathom as opposed to a calculator or another program allows the students to more easily test for significance without have to input everything into lists, since the lists are already made out. This way they can spend the bulk of their time trying to figure out why stuff is the way it is opposed to spending the bulk of their time inputting data.

3. Describe how the technology affects student’s thinking processes.

Thestudent will see the graphs of each and think that there might be a significant difference between the two tracks. Hopefully this leads them to question why there is not a difference try to figure that out.

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

Reflection

Lesson Plan Template MATE 4001 (2013)

Title: Is there a significant difference between wooden and steel roller coasters

Subject Area: Statistics

Grade Level: High School

Concept/Topic to teach: Testing for the significance between two means

Learning Objectives:

Content objectives (students will be able to……….) Students should be able to figure out if there are any significant differences between wooden and steel roller coasters and understand why there is not even though there appears to be a large difference in some of their distributions.

Essential Question

What question should student be able to answer as a result of completing this lesson?

Is there a significant difference between wooden and steel roller coasters? Also what factors contribute to the fact that there isn’t any significant difference although it seems there is a difference in the distributions.

Standards addressed:

Common Core State Mathematics Standards:

CCSS.Math.Content.HSS-IC.B.5 Use data from a randomized experiment to compare two treatments; use simulations to decide if differences between parameters are significant.

Common Core State Mathematical Practice Standards: CCSS.Math.Practice.MP1  Make sense of problems and persevere in solving them.

CCSS.Math.Practice.MP2  Reason abstractly and quantitatively.

CCSS.Math.Practice.MP3  Construct viable arguments and critique the reasoning of others.

CCSS.Math.Practice.MP5  Use appropriate tools strategically.

CCSS.Math.Practice.MP6  Attend to precision.

Technology Standards: Copy and paste from NCDPIHS.TT.1.1 Use appropriate technology tools and other resources to access information

(multi-database search engines, online primary resources, virtual interviews

with content experts).HS.TT.1.2 Use appropriate technology tools and other resources to organize information

(e.g. online note-taking tools, collaborative wikis).

Required Materials:

List all materials needed for your lesson

Computers

Fathom

Notes to the reader:

Students should already have been introduced to a significance test.

Time: Assume 60 minutes ***

Time Teacher Actions Student Engagement

Introduction

5-10

I will review how to take a significance test on Fathom at the beginning of the period and then introduce the data. From here I would ask the students about different roller coasters they have been on and their experiences on them and which their favorite is. After each response I will try to find out what kind of coaster it was and then pose the question are there any significant differences between the wooden and steel coasters.

Tell them that they have access to data on certain roller coasters and

Students will be answering general questions on roller coasters, like which their favorite is and details about them, specifically wood and steel.

that I want them to answer my question. They are to create a graph of the data and perform the hypothesis test.

Investigation

30

Circulate the room to see how everyone is doing. Answer questions if need be. Ask questions to figure out their thoughts.

Students will be creating graphs of each category with steel vs. wood and performing significance tests of the data. They will be interpreting their results to determine significance.

Small Group discussion

5 min

Pair up and share their thoughts on the data that they just analyzed. Have them focus on what their results were and why they think they obtained those results.

Students will discuss their observations.

Large group discussion

10

“What were the significant differences between the wood and steel coasters?”

None

“Type up why you think that is to turn in. And what could be done to get a result with less of a standard error?”

Too small of a sample/need a larger sample

Outliers mainly in the steel category considerably reduced the means of the steel coasters and raised the standard deviation, leading to a much smaller test statistic.

Students will type up their responses to the posed question to turn in.

*** Your lesson plan should ALL be included here (the reader shouldn’t have to go anywhere else to find the plans.) The teacher should be able to read it chronologically. The only things to be included at the end of the plan are supplemental artifacts (e.g. handouts, tech files, ppt). If you chose not to use the table then the time, teacher actions and student actions should be clearly noted throughout your plan.

Make sure that your lesson is detailed enough that someone else could teach from it. This is especially important during class discussion phases. For example, be sure to detail what the teacher should be sure to bring out in a whole class discussion, including questions to push students to build conceptual understanding, questions to assess student understanding, and transitions between portions of your lesson.

If students are working in pairs / small groups this should be noted (including how the groups are to be determined)

All tasks / examples should be worked out and included in the body of the lesson plan All HW should be worked out

Reflection

Going through this lesson on Fathom I found it very easy to perform the tasks that were

presented. It was very easy to graph each category and display each as a scatterplot and also to

perform the hypothesis test. The ease at which you can do that allows the students more time to

try and interpret both the graph and the results. The one drawback I found was that when I read

through the hypothesis test, there is so much information presented in a small area that I felt

overwhelmed and it took me a couple minutes to sift through everything that had been given and

figuring out everything and what it meant. For the students it gets rid of the tediousness of

finding/entering all the data and allows them more time to work on the inferential part of

statistics (which is what statisticians get paid to do). The only drawback is that in having

everything instantly, students could lose the meaning behind each of the statistics that are

brought up and how concepts are interrelated and affect each other.