Module 6

Hey Jess!
I hope you're having a great week! This has probably been my favorite module so far. I remember doing box plots in school, but it has been a while and this module gave a great review! I also always like looking at example lessons, so that is a nice resource to have!

Box Plots

In the box plot shown to us in the talk over PowerPoint, I personally believe that Class A would be easiest to teach a follow up lesson to. As an estimate, the minimum of this class is around 32, the first quartile around 40, the median around 44, the upper quartile around 50, and the maximum is around 60. This essentially shows us that the tests scores range from 32-60. This may seem large, but it is not nearly as large as the other class, who ranges from around 19 to 100. Knowing that all of the students performed poorly in Class A and had a smaller range of scores, I believe it would be easier to teach them a follow-up lesson and take time to cover areas of the test again. When all of the students perform poorly, something must not have been covered properly the first time. With Class B, it would be hard to cover all of the material that students who received very low grades might need, especially knowing that a majority of the students passed and some got As, so they do not all need the review. Can you think of any reasons that it would be better to teach Class B? I was torn, because while more students succeeded in Class B, I always find it easier to teach students in the same range of knowledge.

Above, you can see the boxplot I made comparing the German class's data collection of trash weight to the class given in the scenario. Here are some questions I believe a class could answer using this data:

1. The German class clearly has lower numbers of data than our class. Could the large difference in class size effect this?

My answer: No, class size will not have an effect on these box plots. While we may have gotten different data using more students, the large class size of Germany's class would not have a direct cause-and-effect relationship with its lower numbers.

2. What similarities can you find in the two boxplots and what do they mean?

My answer: The only similarity really is that both of the minimum values are slightly over 30. This only means that at least one student in our class and at least one student in the German class only had around 30 pounds of trash that month.

3. Is it safe to say that on average, a German student had less trash than one of our students? Can we conclude that in total, the German class had less trash than us?

My answer: While we cannot see the mean on a boxplot, it is safe to say that on average, a German student produced less trash. However we can NOT say that we produced more total trash than they did, even though it may appear that way. Seeing as we only had 18 students and they had 43, if we were to total up all of the data, theirs would likely be much greater than ours. 

4. Which class has the biggest range and what does this mean for the data?

My answer: Our class's range was much larger, sitting at 82 whereas the German range was around 60. This means that our class had greater variation in the data and the German students had a more consistent weight between the students. 

Did you find any discrepancies in my questions or answers? Do you think these questions promote higher order thinking? If not, please let me know what I could have done better!

Common Core Standards

My very first impression in reading over the common core standards was that we are given very specific information on what exactly the students should know to do after studying that standard. For example, in 2nd grade the students should be able to " draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put together, take-apart, and compare problems using information presented in a bar graph." This provides a very specific measure to see if students comprehend that standard. Another impression I had was how much more advanced the kindergarten standard was compared to what I thought it would be. They are already expected to classify data into categories and sort them. I thought kindergarten would be more of an introduction to data by simply collecting data in the class or something like that. Did that surprise you as well?
It seemed to me that in each grade, a new step was added to coincide with the curriculum. For example, the data standards in 4th and 5th grade are very similar, but in 5th grade they are to use harder operations of fractions with the data given, whereas in 4th grade they just need to add or subtract fractions. The data standards consistently increase while new steps are added.
As for rigor and complexity, I think that kind of goes hand-in-hand with what I just mentioned. The complexity of the expectations increase with each grade, but not to an insane point. It is almost as if the data standards increase a  bit each year and pieces of their other standards are thrown in. In the example I gave above about 4th and 5th grade, they are expected to know operations of fractions in 5th grade, so that is now thrown into their data standards as well.

In comparing Common Core standards to NCTM standards, I find Common Core to be a little more specific in expectations. However, I do see that the main areas of each grade or grade level band are outlined in each. For example, in K-2, you see classifying, sorting, representing, and describing the data in both Common Core and NCTM standards, but Common Core goes more in-depth to what kind of graphs they should be able to create and how many categories should be in these graphs. However, in 3-5, the Common Core standards focus more on using operations in the data given, while NCTM talks about designing investigations, which is not even mentioned in the Common Core standards. I feel that they both give a basis to the statistical process. Both sets of standards discuss collecting, interpreting, and understanding data.

Curriculum Resources
I chose the Grade 1 lesson plan: Would You Rather?

When using this activity, what mathematical ideas would you want your students to work through?
The goal here is for the students to work on data collection, classifying data into groups, representing data, and understanding data.

How would you work to bring that mathematics out?
In the lesson, it talks a lot about discussing as a class what colors can represent which answers and why they should be chosen. Allowing the students to brainstorm ideas on how to represent the data and explain why they would do it that way allows them to reflect on and broaden their decisions. Talking as a class and asking questions about the data will pose questions for the students to analyze the data and show if they understand.

How would you modify the lesson to make it more accessible or more challenging for your students?
To make it easier, things like how the data will be represented can already be decided by the teacher. Rather than brainstorming and deciding on these things as a class, it can just be told to them so they know what to do. To make it more challenging, you could add more answer options to have more categories, or have the students come up with alternate answers.

What questions might you ask the students as you watch them work?
One of the best questions to ask students in situations like this is "why?" We discussed this in an earlier module, but while the students are deciding what they want to investigate, it is important to point out what could go wrong or if the question could be worded better. Rather than pointing things out to them directly, asking why they want to know that or what exactly they are trying to discover could help them make their question more specific. Simply asking the student to explain "why" can help them reflect and make better decisions once they thought it through. Asking things like "how do you plan to collect your data" or "how do you plan to represent this data" can get them thinking ahead.

What might you learn about their understanding by listening to them or by observing them?
In asking the students to discuss as a class or by listening to them talk with their partners, it will be clear if they understand the task at hand and the data that has been collected. It is important to pose questions to get a gauge on their understanding, but seeing how they interact with their partners can also show what their strengths and weaknesses are in the topic. If a student is frequently asking their partner to explain something to them, then maybe that student does not have a clear understanding of why something happens a certain way.

How do the concepts taught in this lesson align to the Common Core Standards? 
The first grade Common Core date standard is to be able to organize, represent, and interpret data. In this lesson plan, students must do all of this. They organize the whale vs. eagle data as a class and represent it in different ways, like using colored cubes as proposed in the lesson. They also investigate their own question and choose how to interpret that data once collected.