Module 5

Hello again everyone!

  This week's module covered some information that I really didn't know before. I honestly can't remember if I was ever taught to use Box Plots before, so it was interesting to learn about them now. Also, the information about teaching math that aligns with the Common Core State Standards was enlightening. I will use this blog entry to share my thoughts and opinions on the activities and questions brought forth in this module. The headings in bold red are items that are required for this blog.

Box Plots Introduction--Voiceover PowerPoint

        I think it is interesting that Box Plots are designed to give people a visual representation of the mean and other values from a set of data. It was great be guided through the process of creating a Box and Whisker Plot since I have not done so before. Below are pictures of my work when finding the necessary values to graph my plot for the Houston Rockets activity along with a picture of what my box plot looked like after completion.

Here are images of the work I completed when I created the box plot for the players' heights.

      Next, the task was to create a box plot by tweaking the data set a little. We were instructed to take out one piece of data--Yao Ming's height. Before doing this, I considered the questions that were raised:

What will happen with the extreme values?
   Only the upper extreme (maximum) will change because Yao Ming's height is the upper extreme. The lower extreme will not change because John Lucas III's height (the lower extreme) is not being taken out.

Do you think the box plot will look dramatically different? Why or why not?
 Not really. At 90 inches, Yao Ming is the tallest player on the team but he only has a 4 inch advantage over the next player that is below him in height. Taking out Ming's height wouldn't show too much of a difference.

After having both box plots shown in the PowerPoint, I was interesting to compare and contrast them. I considered the questions from the presentation:

What happened to the median?
   The median stayed the same. Taking out Yao Ming's height did not affect this value.

What happened to the extremes?
   Just as I predicted, only one extreme changed (the upper). The lower extreme stayed the same because we did not remove this value.

What happened to the upper and lower quartiles?
    I had expected to see a change in at least one of these values because there was now an odd number of heights. The lower quartile did not change but the upper quartile barely changed from 81.5 to 81.
What happened to the mean? Why?
    I hadn't expected a big difference in the mean considering that Yao Ming was only a few inches taller than the next tallest player. The mean with his height was 79 inches. Without his height, it was around 78 inches.
   
What affect does Yao Ming have on the range and the mode?
    The range was significantly changed after taking out Ming's height. Before removal, the range was 19 inches (90-71). After, it was 15 (86-71). The missing height had no affect on the mode of the data set.
 

 

 

More Practice With Box Plots

  It was nice to receive more practice with Box-and-Whisker plots thanks to the summary lesson provided in this module. I was able to read over this and gain a better understanding of how to use and analyze these plots. I will say that I was fine up until I got into the part about finding the outliers in a set of data. I understand the concept and was able to figure out the solutions with the answer key. I have never worked with his kind of information before so this is all new to me. Although you all worked through the problems and know the answers, I have provided images of my worksheets so you can take a look at how I did them. Did anyone else struggle with parts of this assignment?

 

 

 

 

Box Plots--Another Scenario to Consider

    The Module 5 checklist presented a different box plot scenario that involved the amount of trash families discard each day. I have decided to share my work for the questions asked for you all to see.

a) Make a box and whisker plot for data in your class and draw it under the German class's plot using the same scale.

Work:

b) Suggest three good questions that you could ask your class in making comparisons between the two plots. Answer your questions.

           Possible questions:
         1) What does the difference in ranges for each class tell us?
                Answer: The range for our class appears to be much larger than the range for the German class. The lowest points are close together but the highest points are very different. This indicates that there were people in our class that had trash weighing more than the maximum weight of trash from the German students.

        2) What does the difference in medians for each class tell us? Why could this be?
              Answer: The median for our class (83) is drastically different from the median of the German class (around 55). The big difference could be caused by us having only 18 students and the German class having 42 students.

       3) By only looking at the plots, would it be fair to assume that individual people in our class
             throw away more trash per day than the students in the German class? Why?
             Answer: No. Because you don't know the exact number of students that were polled in each class.

Do these questions seem okay? What other questions can you think of?

           

Common Core Introduction

 

       Considering that I will complete my education courses this semester, I look back on my experiences in previous courses and realize that I have learned so much about the standards and objectives that associated with the curriculum teachers are responsible for teaching. I EDN 322, I recall going over the standards for math and relating them to lessons and activities I could use in my future classroom. I did take some time in this module to read up on the standards for data and statistics and explore the links that were provided. The PowerPoint was also helpful. I was reminded of the different domains of development required by the standards for specific grade levels (Operations and Algebraic Thinking, Number and Operations in Base Ten, etc.).

NCTM and Common Core

Looking only at the Common Core Standards respond to the following questions or statements:

    Write down two “first impressions” you have about the standards:

        1) The Common Core descriptions are very detailed. Some categories show specific examples of
        problems children in each grade will be asked. These will be super helpful when planning lessons that
        focus on the given objectives.

        2) I noticed how easy it was to identify the standards for each grade. I like how you can simply look at the
         domain (Measurement and Data) and see what standards are reserved from a particular grade (i.e.
         K.MD is for Kindergarten, 1.MD is for 1st grade, etc.).
 
    How do the concepts progress through the grades?
          I think the amount of requirements appears to increase as the standards progress. With each increase in
          grade level, students have more standards or clusters to meet. I visited the Common Core website and
          read over some of the other standards listed under the Measurement and Data domain
          (http://www.corestandards.org/Math/). Kindergarten students only have 3 standards and 1st graders
           have 4. I noticed a huge jump from 1st to 2nd grade because there are 10 standards for this level. Third
           grade students also have a large number of standards to meet: 14 (this includes the sub-topics). I could
           be wrong, but perhaps this has a lot to do with the standardized testing students take in 3rd grade and
           up. The large increase in standards for 2nd grade may occur to prepare students for the tests.

    How do the concepts change and increase in rigor and complexity for the students?
          I do think that the concepts become increasingly harder for students to work through and understand. In
          each grade, students have new ideas/concepts to learn like representing time, taking measurements,
          constructing graphs, interpreting/analyzing data, etc. Most of the information is a continuation of the
          standards in the grades but it seems like students might not be able to keep up with the material.
          Moreover, I see that students in 4th grade are introduced to solving problems from line plots with
          fractions. This seems like a rather complicated task for children at this level.

Now look at both the Common Core and NCTM standards to respond to the following questions:

     Does the Common Core Standards align with what NCTM states students should be able to know
     and do within the different grade level bands? (Note that NCTM is structured in grade level bands
    versus individual grade levels.)
          For the most part, yes. Since the levels are set up differently, it took me a little bit to compare the two
          sets of standards. However, I will say that the NCTM standards were easier to read through than the
          Common Core. The NCTM standards were shorter but still listed important information. The CC
          descriptions are written to where you kind of have to "pick" through the content  
     
    Give examples of which standards align as well as examples of what is missing from the Common 
   Core but is emphasized in the NCTM standards and vice versa

       I found many instances where the NCTM standards aligned with the Common Core. For example, the CC calls for students to “classify objects into given categories” (Kindergarten), “organize, represent, and interpret data” (1^st grade), and “draw a picture graph and a bar graph (with single-unit scale) to represent a data set…” (2^nd grade). All of these things are similar to the NCTM’s requirement for students to “sort and classify objects according to their attributes and organize data about the objects” (K-2) and “represent data using concrete objects, pictures, and graphs” (K-2). Both sets also mention for students to ask and answer questions about data. On the other hand, I do notice some missing items when looking at both standards. The Common Core requires that students know how to “generate measurement data by measuring lengths of several objects…” (2^nd grade) but I see no mention of measurement in the NCTM standards—even for the upper grades. One thing missing from the Common Core is that children are not required to develop and evaluate inferences based on data (NCTM standard for K-2). I think this is an important item because this can help make learning relevant for students.
     Looking at the standards in the 3-5 grade band, I found that both the Common Core and NCTM standards require students to be experienced in their knowledge and ability to use graphs. Third grade Common Core standards deal with drawing scaled picture graphs and bar graphs. This reminds me of the NCTM standards that call for students to “represent data using tables and graphs such as line plots, bar graphs, and line graphs”. In my opinion, the NCTM standards seem to focus more on data analysis and interpretation than the Common Core. I think the Common Core standards (or at least the ones that were given to us) place more emphasis on the act of drawing graphs than making sense of the actual data. That is just my observation. Another difference I noticed is that the NCTM standards require students to know about “measures of center” like the median. I saw no mention of this in the Common Core.

   Interestingly, it seems as though students in 6^th grade make the transition from learning about graphs to actually interpreting them with statistics (in the Common Core). They practice analyzing distribution and learn to identify important measures or values in a set of data. Recognizing appropriate statistical questions and understanding “that a set of data collected to answer a statistical question has a distribution…” is something that is emphasized in this grade. This aligns with the NCTM’s call for students to “formulate questions, design studies, and collect data…” (Grade band 6-8). With both sets of standards, students should be able to understand and interpret data in other types of graphs like histograms and box plots.

   

Curriculum Resources 

 

  

          For this activity, I chose to work through a set of sessions entitled “Would You Rather?” I thought this was a great lesson that helped students understand the use of surveys, practice their skills with inventing representations of data, explaining/interpreting results of surveys, and making plans to gather and record data.
 

Description: 
    The lesson begins by describing how one class has been spending time learning about sorting objects and people into certain categories. Students learned that one way to separate people is by conducting surveys—or simply asking them about what they think or what they do. It was also emphasized that surveys can reveal important or interesting information we are wanting to know. The teacher in the scenario then presented students with a survey question they would use to guide an investigation in the classroom. The question: Suppose you could be an eagle or a whale for one day. Which one would you be? Before gathering responses, it is suggested to talk about eagles and whales by sharing pictures of the animals and having students really think through their decisions.
        Interestingly, the activity calls for the use of colored cubes (and something called Kid Pins?) to help students keep track of the data they collect. The different colors would represent eagles and whales. The cubes are presented to the class with sticky notes to label each group. After collecting and sorting the data, the class discusses the results and analyzes the information they collected.
      Next, the lesson allowed students to come up with their own representations of the data. Students chose from a variety of materials like paper, pencil, colored cubes, sticky notes, etc. to visually share the data gathered from the class. The document actually provides a few examples from children that are actually very interesting.
   Finally, the teacher in the activity’s description has students partner up to work through a different survey question that he/she provided (students do have the option of creating their own questions). Each pair of students is given a sheet called “Our Plan for Collecting Data” (shown below) that guides them to think about how they are going to survey their peers and keep track of the data. 
     

Required Blog Questions:



1. When using this activity, what mathematical ideas would you want your students to work through?
      I think this activity presents a few mathematical ideas and concepts. I would want to my students to understand ways we can collect numerical data by asking questions in surveys. While this particular activity's question doesn't yield numerical data, students learn they can organize the data to get a numerical value. I think a lot of the mathematical ideas surface when students begin to explain and analyze these results. I would want them to realize that their representations can help answer questions regarding the most popular option and how many more/less people voted a certain way.   
2. How would you work to bring that mathematics out?
     I would have students learn about data collection by simply letting them experience being part of a survey. I would also use a lot of examples. I like the way the teacher in the lesson's description used a variety of methods and visuals to help students show the results of the survey. Next, I would have children share their representations and initiate a class discussion about what they see. I think this is where students gain a better understanding about what the results mean because they listen and add on to their peers' thoughts and explanations.

3. How would you modify the lesson to make it more accessible or more challenging for your students?
    I am unsure of the ways this lesson could be made more accessible since it appears that students have access to a variety of materials and opportunities to work/discuss with their peers. To make the lesson more challenging, I would have students come up with their own survey questions instead of them selecting from a group of prewritten ones. This may require a little extra time but I think the brainstorming they do can help them think about the importance of developing a good question that gives two or more options. Simply extending the list of options from which people can choose can be a little more challenging, too. For example, students could add on an animal: "would you rather be an eagle, whale, or cheetah?".

4. What questions might you ask the students as you watch them work?
    a) I could remind students to be mindful of whether or not they are grouping the data correctly. I could ask them if they think their categories are specific or if they need to be changed.
    b) "Are you sure you counted the data correctly?" "Does the number of the data match the number of people in the class?" I think this is an important one because a lot of students can either lose track of the data points or miscount, thus resulting in an inaccurate representation of the data.
    c) "How can we make collecting and counting the data easier?" "What strategies can you think of?" I think this would be an interesting question to ask because each student might have a different way of making sure they collected accurate data.

5. What might you learn about their understanding by listening to them or by observing them?
    I would say that it would be easy to get an idea of how students are understanding the material by observing them as they work through the sessions. The final part of the activity that requires pairs of students to conduct their own surveys using a different question would allow peers to share their thoughts and potential plans. Listening to their ideas for how to collect and represent the data would help me understand what they got out of the initial lesson. I might learn that some students grasp the concept of collecting/representing data when they effectively and accurately record individual responses they gathered from the class. I may also overhear these students talk about displaying the data using a variety of methods that were discussed in the class. I might learn that some students need more time understanding these mathematical concepts when I observe them struggling to come up with a plan to collect the data.

6. How do the concepts taught in this lesson align to the Common Core Standards?
     For this question, I went back to the Common Core State Standard's website to read through the listed items that might align with this activity. I found that the lesson can be applied to the Measurement and Data standards in Kindergarten and 1st grade:

CCSS.Math.Content.K.MD.B.3
Classify objects into given categories; count the numbers of objects in each category and sort the categories by count.¹

CCSS.Math.Content.1.MD.C.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.

   I saw the need to not include standards for 2nd grade and up because the concepts they addressed went a little beyond what this lesson covers. Starting in 2nd grade, students learn how to measure lengths, draw scaled bar graphs, and work through word problems using graphs. I thought this was a little too advanced for the target age of the students from the lesson I shared. Nevertheless, I think the lesson does a great job of emphasizing the requirements for the Common Core standards for Kindergarten and 1st grade. Obviously, the activities involve the classification of objects, counting and sorting objects, organizing and interpreting data, and asking/answering specific questions about the data.