8PM EST---CORRECT ASSIGNMENT

SECTION 1

REPLIES TO PAM, MEGHAN, STACY : Engage in a meaningful discussion of the student’s understanding and the pedagogical approaches for each situation. You might also make connections to your own teaching. Would you expect a similar response from your own students? If not, why not?  Have you experienced similar questions in your own classroom? If so, how have you handled them.

pam

Student 1--

 Problem D2 showed two box plots, one for the boys’ heights and the other for the girls’ heights.

In Problem D2, Monique stated that: "It looks like just 12.5% of the boys are taller than all of the girls, and maybe about 10% of the girls are shorter than the shortest boy."   That was not a correct interpretation of the box plot.  12.5% is half of 25%, so Monique might have got that value from an understanding that box plots can be broken into four groups of 25% of the data.  I think the 10% value was an estimate.  The difference between the shortest and tallest student was 14 inches.  The difference between the shortest boy and shortest girl was 2 inches.  The ration of 2 to 14 is not the same as 1/10, but I wonder if the height values are what she used to estimate.

 

My next instructional move would be to ask Monique how she came up with the value of 12.5%.  I would find out if Monique knew how the box plots were created and how to interpret the results.  I would provide Monique with the boys’ raw data or have her create the data set from the dot plot.  I would ask Monique to tell me what a box plot represents and what the different parts mean.  I would ask her to show me how to find the five-number summary, all the while scaffolding any parts she needs help with. Finally, I would ask her to compare the data set broken into four groups to the boys box plot and I would ask if her thoughts on the boys’ data changed and how.  I would also ask her how she came up with the 10% value and possibly have her redo the steps with the girls’ data.

 

Student 2

 

In Problem D2, Arketa stated that: "There is a lot of overlap in heights between the boys and girls."  That is a true statement, but it is very broad.  Is Arketa talking in terms of the middle 50% of the data or the full range of the data?

 

My next instructional move would be to ask Arketa for more information.  Where does the data overlap?  How does it overlap?  Why is it significant?  Is the overlap of the boxes the same as the overlap of the whiskers?  Why or why not?  What does that mean?

--Meghan

 I looked at the K-2 strand.  In this strand there were many student obsevations about the data they collected. Below are the two reponses I chose to discuss.

Sahar: "I think there will be between 32 and 38 raisins in that [unopened] box because most of our boxes had between 32 and 38."

This student clearly understands the idea of using what they observed to help make a prediction.  Thes student was able to look at where the data was "clumped" to help understand that most of the boxes they opened had this number of raisins. My next step with this student might be having them try to find the median.  This would help the student to find that middle value so that maybe they could use one value to make a prediction rather than a range of calues.

Isaiah: 

"Look at that gap with the blue dots -- and there aren't any gaps on the green dots."

This student is looking at the data and definitely comparing two different graphs.  This student had a more observant response than some of the other classmates because they were more fixed on the vertical aspects of the data while this student also looked at the spread.  My next step for this student would be to get them using the correct vocabulary.  Have the student use spread, and outlier to talk about this data.

Stacy…..

Hi All,

I teach second grade so I looked at the data and case study for the K-2 interval. My observations about the studnets are included below.

Sahar and Paul- Mr. Mitchell’s Class

Sahar: "I think there will be between 32 and 38 raisins in that [unopened] box because most of our boxes had between 32 and 38."

Paul: “I think there will be 34 raisins in that [unopened] box, because 34 had the most." 

I think these two students demonstrate an understanding of central tendencies and ‘typical’ values when they make predictions about how many raisins would be in an unopened box. The idea of the mode being the value that appears most often is evident in Paul’s response and the idea of most of the data being contained in a cluster is evident in Sahar’s response. Both students accurately use these measures to make predictions about the unopened box of raisins.

Since these students seem to have a good understanding of how to interpret the data and identify ‘typical’ values the next step would be to assign statistical vocabulary such as ‘mode’ and ‘cluster’ to the concepts that each student highlights. Additionally, I may present these students with a data set that appears to be bimodal (maybe the second pocket data line plot) to see how they use what they know about modes and clusters to identify ‘typical’ values.

 

Ramel: Mr. Mitchell’s class

Ramel: "The range is from 25 to 43." 

From this statement it is clear that Ramel has a misunderstanding relating to the meaning of the vocabulary word ‘range.’ His statement indicates that he considers the range to be the distance between the smallest and largest number represented on the axis of the line plot rather than the distance between the smallest and largest VALUE represented on the line plot. He does however have a foundation for understanding the range as he understands that it encompasses the distance between two values; namely the smallest and largest.

The next step for Ramel would be to review the meaning of the term ‘range’ and how it is found. His current statement has simply identified the interval for the range, he has not actually calculated the range (difference between the largest and smallest value). I may give him a few examples of the range, then have him work with a buddy to find the range on his own with other data sets and then return to the raisin data and ask him “after reviewing the term range can you revise your statement about the range of the raisin data?” This way he will be able to see and correct the error he made previously.

SECTION 2

REPLIES TO #1,2,3,4: Make strong connections between the course and your practice. Take this opportunity to wrap it up together, in a nice bundle you can walk away with!

1. BRING IT BACK---RICHARD

I am going to write this as if I were meeting with my 7th grade teaching peers.  We really work well together and enjoy bouncing ideas off each other.  

While much of this course dealt with concepts above our students expected knowledge level.  I am going to address the parts that I would expect them to know or be able to learn.  This course started with a review of measures of central tendency.  This is more of a 5th/6th grade standard in Massachusetts, but it is important to review these concepts to ensure understanding.  I am constantly surprised at how much students forget over the summer.  It is important for students to be able to create and analyze multiple   representations of data in the form of bar graphs, histograms, box plots, scatter plots, and frequency tables.  In addition, using technology to create these representations will allow more time thinking about the meaning instead of the creation of these models.

Once these models are created, students need to be able to identify and quantify the spread.  Specific application to our grade level would include IQR and MAD.  Standard deviation is something they will calculate in high school, but it is important to know what they will be learning in years to come.  If the opportunity presents itself, we can expose them to this concept.

One other concept that applies indirectly to our grade level is probability.  In this course, we looked at probability through the Empirical Rule.  This could tie together probability and even solving equations.  I would not expect them to understand the Empirical Rule, but they should be able to find probabilities from given standard deviations.  I would envision this as an enrichment activity because of the attention to detail needed to solve these problems.

Also as enrichment, we could discuss bivariate data.  This is a major concept in statistics and probability in the 8th grade curriculum.  It can be an extension of representing proportional relationships in a graph, table, or equation.  It would be an opportunity for them to see that in the real world, data doesn’t always fall exactly into an equation and we have to apply the line of best fit.

There are two specific parts of this course that I would present to my colleagues.  The data set and questions on How Do Students Value Statistics is a rich activity with specific application to 7th grade.  I also really enjoyed all the Annenburg segments.  They are well developed and lead students through the discovery process.  Ultimately this is a better way for students to learn.

2. RANDALL

There is so much that I have learned in this class.  Statistics are part of everyday life and for you to get the most out of the data that is given to each and every one of us it is imperative that we know how to read and interpret the data.  Data can be manipulated so that whatever the entity that is presenting the data can make it look so that the data will support whatever agenda that entity has.  Knowing the difference between the mean of a set of data and the median of the set of data can make all the difference in the world on the interpretation of that data.  Knowing the Empirical Rule makes it very easy to predict the probability of an event occurring.  Standard deviation allows one to see which data is truly important and which data doesn’t have an effect on the process.  Just today in my Algebra 2 class we are taking data, making a scatter plot, finding the trend line, the equation of the trend line and the correlation coefficient.  I am doing all of this on the TI -84 Plus calculator and the students are amazed at the results they are getting.  I have already, on the third day of school, used what I have learned in this class and I am much better prepared to explain any questions that the students have.  I would recommend this class to any math teacher in the secondary level so that he/she can become a better teacher and prepare our students today to life tomorrow.

3. PAM

This course has shown me how critical it is for students, and adults, to understand how to interpret and how to use statistics in everyday life.  The statistics strand in math is one that we encounter and apply on a regular basis.

 

There are many things from this course that I can bring back to my classroom.  Things that come immediately to mind (in no particular order) are vocabulary, how statistics fit into the common core standards, activities and applets used in this course, the meaning of center in a data set and using a project to apply the concepts we learned.

 

All of the vocabulary that we learned during the first week seemed overwhelming.  I could not tell the difference between a variable and an observational unit.  As the weeks went on, the new words became part of my own vocabulary.  Our students benefit from exposure to math vocabulary on a constant basis.  Another thing that I will bring back to my practice are the newfangled ways to say box and whisker plot (box plot), stem and leaf diagram (stem plot) and line plot (dot plot).  I noticed the newer versions of those terms as I went through the common core standards for the grades below and above mine, so now is the time to use them!

 

Some of the Annenberg activities (such as having students use the number of people each lives with to create a data set for summarizing and graphing), and applets, are pertinent for teaching statistics in 7th and 8th grades.  In 7th grade we work with measures of central tendency and measures of variation (MAD, in particular) and in 8th grade we use bivariate data to create scatter plots and find the line of best fit (an approximation, only).  Some of the applets show how to cut to the chase, so to speak.

 

I can also use ideas from the NCTM articles we read.  Finding a balancing point in a data set might help my 7th graders be able to put mean, median and mode into context.  Using the previously mentioned family size data to help students understand how distribution works can lead into our unit on MAD, as it did in the article.

 

Finally, conducting a study or doing a class project is an excellent way to assess student understanding of concepts as we go along.  From my own experience, applying what I have learned to a study of my own design has made the material far more relevant and interesting.  I believe it would have the same positive impact on my students.

4. VIRGINIA

The main message about teaching statistics/data analysis with my colleagues is that we are really nurturing and teaching analytical thinking. As the grade level increased, I noticed that the skill set went from being able to construct and represent data(1st grade/2nd grade) to analyzing what the data means and more complex mathematical calculations. For example, in third grade students were working just with whole numbers for their data set. In fifth grade, the data set included fractional units and using operations of fractions to solve/analyze the data set. Sixth grade marked when students really started to dive into the type of analytical thinking that we have covered in this course (though in the younger grades this type of thinking is introduced in an age appropriate way). This week really illustrated to me that problem solving and statistics go hand in hand.  Watching the video with the fifth grade class, the students were able to calculate the mean, median, and mode but lost the context of the problem and what those terms told them. That type of questioning is something that is integral to statistics and data analysis and should be the focus of instruction. However, I do not think that video was an isolated example. Teaching analytical thinking is difficult for students to grasp as it involves higher thinking level skills and something beyond just memorization. However, analytical thinking and asking “What is this telling me? What is this NOT telling me?” and even “What are the limitations of this calculation?” are integral in teaching statistics, data analysis, and probability.

SECTION 3

PEER REVIEW—PPT ATTACED

Comparative Study

Peer Review Rubric ____/15

Criteria	Assessment
	Completely Addresses	Mostly Addresses	Somewhat Addresses	Does Not Address
1. You thoughtfully completed the “Peer Review Feedback form” for two studies. (3 pt)	3	2	1	0
2. Your comments reflect an understanding of the content of the course. (3 pts)	3	2	1	0
2. Each Peer Review provides at least three specific pieces of meaningful positive feedback. (6 pts)	6	4	2	0
3. Your Peer Reviews provide specific meaningful suggestions for improvement. (3 pts)	3	2	1	0

Peer Reviews