ImagineIT Phase V - Conferring with Colleagues & Student Focus Group Feedback

 
     In communicating with a couple of teachers, my dilemmas were validated. The math department coach said, ‘I think the pacing issue is a daily struggle with how much is enough.’ My co-teacher told me that, ‘I think we could introduce fractions on the number line (i.e. where they are placed) when they are given a fraction solution.’ Implementing this suggestion will allow students to see the value of the Real Number Line as a visual for an abstract concept, like a fraction. In terms of allowing students to retake assessments, the math coach wrote, ‘I think you should offer retakes all the time.  I don't think allowing the students the opportunity to demonstrate mastery repeatedly is bad.  Think about what your goals are.....you want the students to understand and show you [mastery].  Does it really matter how many attempts they take to get there?’ My co-teacher offered, ‘I like your idea about replacing their lowest quiz grade when they show improvement on the unit test.  I think you should keep with this idea!  This way, they do get one "pass" if they struggled to learn one concept, but they still have to show mastery on the test...’
     A focus group comprising nine students met before school last Thursday to discuss my ImagineIT project*. When I asked students about their interest in learning numbers more deeply, they offered these thoughtful responses:
  • How did numbers come to be?
  • Is there another way to add, subtract, multiply and divide? (Immediately, logarithms sprang to mind.)
  • I’d like to explore infinity more because if we start with some of the basics, I’ll understand what we’re doing now even better.
  • We could spend a week building an understanding of the relationships among numbers, which can help us on tests in this class and in future classes.
     The students in the focus group, many of them reluctant learners of math, were energized – as was I – by the idea of exploring number history and theory. They groaned when I mentioned fractions, and I sympathized with their emotional reaction. In spite of their lack of success with or negative feelings toward math, they were interested when I brought up different sizes of infinity, whether numbers were discovered or invented, and the idea that 1 = 0.9999... . Viewing numbers from a philosophical point of view sparked their interest. There was a consensus that carving out a few days to a week or more exploring numbers in this way, as opposed to following the curriculum only, would (a) shore up their understanding of numbers and (b) help them in future math classes.
     Based on the focus group’s thoughts, I want to move forward, especially with my Advanced Algebra with Trigonometry students, with making time in the curriculum to explore number theory in greater detail. This will happen naturally in the next Module in our book, which explores the relationship among number sets. Allowing students to create a project around a number theory topic that interests them (e.g. different sizes of infinity or a short history of zero) is something I feel compelled to do based on focus group feedback.
     I was surprised and heartened by their reaction to the ImagineIT i-Video I created this summer on number sets. They wanted to learn more about this topic and seemed to enjoy the video. Giving them the time and space to create a project centered on topics mentioned above seems like an enriching endeavor that they would enjoy and benefit from.
 
     *Because of limited time and focus, the focus group did not discuss my second dilemma, retaking assessments.