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that this lack of conceptual connection to points also extended to the students not understanding the connection to slope. I had to help all the groups understand that the data points they were defining corresponded to a slope, just like we had been learning in the weeks prior, which could be found by the change in each variable, respectively. How ever, if the students couldn ’ t make the connection to the points, then I wouldn ’ t expect them to make the connection to slope or other graphic or relation al properties of lines. Additionally, I saw a lot of groups confusing the use of a scatter plot with a histogram or bar graph. While most groups contin ued to use bar graphs in their presentation, I ex plained to each of them the difference in the appro priate use of bar graphs and line graphs. The expla nation seemed to resonate with them. Teaching by inquiry always comes with a gam bling element. It is like making the students jump across a ravine, and there is a chance that they jump and miss. Sometimes recovering from a failed “ jump ” is painstaking, but I believe it is worth the risk to be an inquiry teacher. Throughout my practice of teaching by inquiry, I have seen so much greater benefit than disaster come from it. However, one must be ready to recognize when a student is falling short of that jump when they are out on the waters of uncertainty on their own. It may be a misconception or just a misguided think ing process, but the teacher needs to be poised to gently help the students back on track. This process can be exhaustive when monitoring an entire class. My largest class size for an inquiry lesson is 17 people. I am proud of the practical conclusions the students made as they went through this project. All groups used deductive reasoning to synthesize the information they gathered from parents and from the figures they calculated together, to pro duce authentic meaning from the project.

tion to slope, which surprised me, but indicated that I need to do more conceptual development of slope with the entire class. Specifically, the stu dents quickly recognized the method for calculat ing earnings per day, week, and month, but only one made the connection between this rate and gra phing, i.e., I had to help all but one group make the connection between time - and - earnings to data points. An example would be that students under stood one hour yielded $7.25, two hours yielded $14.50, and so on, but only one group (see Figure 2) made the connection between these figures and the points (1, 7.25), (2, 14.50), etc. and how that related to an equation. I had expected students to make this conceptual jump because of the in - depth stock market project I had done with them last year. They had plenty of exposure to graphs and earnings in that project. It stands to reason, then, Figure 1: Example group work showing how some students provided lots of information and was the only group to graph the expenses.

Conclusion

In conclusion, I was pleased with the way this pro ject turned out, but as with all inquiry teaching, the teacher must be prepared to have their expectations altered depending on the level of student success. This flexibility is critical if the inquiry teacher is going to successfully use inquiry in their teaching

Virginia Mathematics Teacher vol. 47, no. 2

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