Week 6

Assignment  6.1.  Pick up math tasks for each of Bloom’s levels. For each task, briefly describe two assessment types you would use.

These tasks are adapted from my week 5 student task assignment (Week 5: 2).

Task 1.  Remembering and Understanding levels of Bloom’s.

The graphs we will work with have data with two variables, an independent (free) variable (often time) and a dependent variable whose value depends on the free variable.  By practice, the free variable is put on the x-axis increasing from left to right.  This makes it possible to visually read trends in the data by glancing from left to right (Assume a lesson, here omitted, on the basics of how to create a graph).  After the lesson, students should be able to understand the graph below.

1. What was the minimum wage in January, 1978?
2. When did the minimum wage reach $3.35?
3. Between what time periods was the largest increase in minimum wage?
4. Based on your observations of the graph, make a prediction about what the wage might be in the year 2000.
5. What about the scales used on the graph might make the data appear differently than how it really is?

Assessment. The material here is the basics of how to read a graph, Remembering and Understanding.  One assessment technique to consider is a standard quiz (like above).  For remembering questions, I might use selected-response or fill in the blanks.  For understanding, a combination of those types with constructed response.

An alternate type of assessment is to have students present different graphs that they find (or are assigned to them) to their classmates.  This would provide another way of assessing how well they are able to read a graph.  This takes more time than a quiz, but it generates more student interest and enthusiasm.  If time is available, it’s worth considering.

Task 2.  Analyzing and Evaluating levels of Bloom’s.

Deciding how to scale a graph is one of the most important decisions to make when constructing a graph.  You need to consider what the motivation for creating the graph is, and just as importantly, how to present the material in a way that is not misleading.  The correct scale to use is closely related to the context of the information you are providing.

These next two graphs show an issue that occurs with scaling. The same issue also occurs in the bar graphs below them.  Can you tell what it is (and can you notice another problem in the top 2 graphs)?

Generally, it you want to present a case of percentage increase or decrease, it is a good idea to start your scale from zero.  If you crop your graph so that just a small range of values appears on the y-axis, you are giving a visual impression that the percent change is greater than it actually is.  This is a misleading technique that is often used when someone wants to sell something, for instance, a business or political entity.

However, there are cases where it makes more sense to restrict the range of the y-axis.  For instance, if you presenting scientific data that was entirely between 600 and 700, then you could consider restricting the y-axis values to be between 600 and 700.  Why would this be helpful?

Assignment. Create at least two graphs from different sets of data you find on the internet.  Scale at least one graph starting from zero and scale at least one graph with a restricted range.

Assessment. In this task, students are to analyze and evaluate what scale to use when graphing data.  They have to analyze what the purpose of the data is.  Then the have to evaluate how to scale it.

One evaluation technique would be for the teacher to give a subjective evaluation on whether they chose the best scaling.

A technique I’d prefer is a constructed response.  The students would be instructed to explain in their own words what the objective of presenting the data is.  Then they would explain why they chose the scale that they used.

Task 3.  Applying and Creating levels of Bloom’s.
Graphing Activity.
Create two sets of misleading and well made graphs with data you discover on your own.  Possibilities for topics include: temperature and global warming, employment and unemployment, per capita income, U. S. casualties in Iraq or Aghanistan, Popularity of a political figure, Average age at the onset of puberty, or any other topic you choose.  Make sure to reference the source for your data.

Assessment. I might change this task to restrict the number of variables being evaluated.  This could be done by providing the data rather than having students seek it.  Then the task is more centered on creating the graphs.

For creative tasks, I like using rubrics because of the guidelines they provide:  Are the axes clearly marked?  Where the correct axes used for the free and dependent variables?  Was the scaling system suitable for the two different problems?  Also, they can give in opportunity for some flexibility in grading.

Another evaluation technique that may work well is self evaluation.  The students could be asked to do their own grading using the same rubric.  Or they could do peer evaluation, grading each others assignments.

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