He wrote "3 + 72 - 6 x 3 - 11" on the board, then asked students to solve the problem in their workbooks and to explain their reasoning, step by step, in simple sentences.
They also recorded this data on a small map of Southern California in their workbooks.
Students in the embedded class also recorded this data on a classroom map in their workbooks.
In analysing the responses of students in their workbooks and in creating plots in TinkerPlots with accompanying text in text boxes, two kinds of criteria were used.
Applying their learning about forces, the students subsequently redesigned a new, group plane and recorded in their workbooks how and why they changed their design.
The class discussion transcripts, however, indicated some students could express in colloquial language ideas that they found difficult to express in written language in their workbooks.
The students created representations in two ways for the data collected in the first scenario, namely, constructing a hand-drawn representation on a blank page in their workbooks and then later using the TinkerPlots software to represent their data.
The basic "Engineering Design Model" (adapted from pbs.org) comprising Problem, Brainstorm, Design, Build, Test, Redesign, leading iteratively to Solution, was discussed prior to the working of the problem, with students labeling the model in their workbooks.
Students' application of critical reasoning, typical of level 4 in the developmental hierarchy of Watson et al. (2003), was not as prevalent in their workbooks as we would have liked.
The students then completed three questions in their workbooks about the recorded measurement values, reflecting Garfield and Ben-Zvi's (2005) development of intuitive ideas of variability and describing variability (phase (i)): 1. Were all of the values the same?
