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dents were self - directed at this point, but the pur pose and direction of the inquiry periodically be came unclear for some students. With light guid ance and clarification, they were all able to get back on track. The most indelible comment from the class period was a student who, seemingly con fused about the project ’ s purpose, came to me and said, “ I don ’ t understand [this project]. We are sup posed to have a minimum wage job and then take on all these bills like a real person would, but I don ’ t see how it ’ s possible. How do these [low wage] people make it work? ” My response was candid: “ Well, a lot of times they don ’ t make it. Or they must work multiple jobs because their boss won ’ t pay for overtime. ” She responded, “ So what are we supposed to learn here? ” I said, “ That is for you to decide. What have you learned so far? ” She replied, “ That minimum wage isn ’ t high enough for people to live! ” I closed the conversation with the question, “ So could you survive on $7.25?” She exclaimed with great authority, “ NO! ” Throughout the class period, others came forward with realizations about the undertones of the pro ject. One student said, “ This whole project is using real numbers for what you make at a [low wage] job and real prices for things you need to live. Is it legal for people to make that little? Shouldn ’ t the employers pay their workers more? I don ’ t think it ’ s fair. ” Another student remarked that, “ I don ’ t think the employers know how much peoples ’ bills are, or they would be paying their workers more. ” Reflections like this peppered the class period as the groups were marching forward with creating their presentations. Most groups chose to use the giant sticky notes and printed out graphs from Ex cel which they taped to the sticky note. Groups decorated their posters with narratives of questions and answers. As I circulated to discuss progress with each group, I was mostly impressed with my students ’ ability to discuss mathematics and at tempt to synthesize information. My students are comfortable with the unknown ethos of “ inquiring within ” when faced with an unfamiliar idea. This is the result of working hard to develop a culture of inquiry; I had made it a regular and integrated part of the class structure and the students become com fortable with the unknown by grappling with it reg ularly.

As the class period ended, students were busy drawing with rulers and yard sticks and working to make exemplary displays of their labor the past two days. I announced that homework for the night was only to keep working if they still needed to finish their presentations. Class on Day 4 was re served for presenting and self - assessing using the Rubric. I reminded the students that they would be grading themselves using the same criteria as I would, and that I would compare their self assessment with my assessment when determining the final grade for the project. I should also remind the readers of this article: in quiry - based learning is up to the student to direct. In many cases, the students do not end up where you intended. “ Could You Survive ” is a good ex ample of this. I intended students to arrive at a real ization about the slope of their income and expens es, and to write linear equations of the two func tions using slope. For example, if a minimum wage worker makes $58 per day, I expected students to realize they could write y=58x as a basic example of the linear equations we had been learning about in class in the weeks prior. However, only one stu dent made this conclusion. There were plenty of other good connections being made between mate rial, but I expected this one, but it didn ’ t end up happening. Students put the finishing touches on their presen tations on the fourth day. There were some disa greements over mathematical process between two of the groups, but one finally conceded that they had made some mistakes in their calculations. Two groups ’ examples are shown to represent some of the work the students produced. Overall, I was satisfied with the outcome of this lesson, but I had expected the students to use more mathematics in their results. One group (see Figure 2) was the only group to write an equation of the earnings, and brilliantly incorporated regular and overtime pay in the same equation. Another group was the only group that made the pay rate connec- Day 4 Reflection

Virginia Mathematics Teacher vol. 47, no. 2

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