"Grow up Count Chocula, Peter Pan..." (10-5-08)

Teaching to ensure deep understanding and covering content are more different from one another then a 65 year-old conservative Republican living in South Carolina and a 24 year old liberal Democrat living in New York City. It's so easy to teach students terms, procedures and algorithms. What's not easy is making sure that each student can take that knowledge an apply it to a meaningful and complex situation. Here's a simple example that brings my dilemma to light.

Consider the mathematical concept of measures of central tendency (mean, median, mode). These measurements provide us with insight into data-analysis and what's really happening with the data's distribution. In addition, they are used everywhere from describing housing costs to corporations using them to recruit new employees. We hear it all over..."The average (mean) salary of an employee working with our firm is $ 78,000, or the median household value of a single-family home in our neighborhood is $ 245,000." The problem with all of this information is that there are factors behind the numbers that most people don't consider. Is there an outlier in the data that may be skewing the average? Who collected the data? From where? With what purpose? Questioning information is part of being a responsible adult. Unfortunately, most adults in our country don't have a strong enough grasp of major mathematical ideas such as the simple one described in this anecdote to really wonder what the numbers they see represent. Literacy is not the same as critical literacy, the ability to synthesize and evaluate what we're reading, not just surfaced level comprehension. So what's my point in this rambling? What should our goal for a 9th grade student be?

To be able to calculate mean, median and mode when given a data set or to be able to think flexibly and apply knowledge and skills related to mean, median and mode?

Consider the following two questions that could be used to assess a student's level of understanding with measures of central tendency.

1.) The following data set represents student's beats per minute during our 1st block class.
- 65, 72, 88, 87, 76, 77, 89, 95, 98, 90, 82, 67, 80, 83
Using the data set, calculate the mean, median, mode ands range.

2.) A data set of student's beats per minutes was collected by a doctor providing physicals for student athletes. The doctor has misplaced some of the recorded data, but knows the following information. Pulses were taken from 14 kids in total and the median beats per minute was 76. The range of data was 31 with a minimum value of 63. The average beats per minute of the students was 82. Using the known information from the collected data, construct a set of data that could represent the 14 student's pulses.


The two questions are both assessing the same content...calculating measures of central tendency. Although not an exceptionally exciting or meaningful problem, the second question asks students to use provided information in addition to their knowledge base of the content to derive a solution. It puts their skills and knowledge to the "test" by asking them to apply what they know to a real "thinking" problem. The first question, on the contrary, simply asks students to follow a procedure that they have previously practiced over and over.

The issue...which question should be our baseline. Is it enough if all of the students can answer the first, or should we raise the bar and demand that all of our students can do the second. As a follow up, were we to choose the second of these two options, where would we find the time to ensure this kind of deep understanding of essential content for all of our students.

If your thinking aligns with mine (even in a small way) then you may be considering using the second question as our benchmark for true content mastery. It would make sense that in an ever changing global economy that places a premium on critical thinking, creativity and problem solving that we would make this choice without question. However, knowing this simply adds to the stress and fear of our job as teachers. We know our student populations and for many of us who teach in the urban environment it's easy to dismiss our ambitious agenda as a dream that can't possibly come true. Quoting Owen Wilson in one of his finest roles a colleague may look at us and passionately cry "grow up Peter Pan, Count Chocula, I want to be cowboys from Arizona or pimps from Oakland, but it's the fourth quarter of the big game" and you're talking crazy.

So my question to myself and perhaps more importantly to you...how do we get students to all engage and successfully conquer question number 2 and move past question 1 where the uneducated adult society currently resides.