Unit Overview: Preparation for Future Learning (PFL)
Teaching across the Thinking with Data (TWD) unit is grounded in the Preparation for Future Learning (PFL) approach (Bransford & Schwartz, 1999). Basically, the PFL approach argues that certain kinds of conceptual learning are more likely to occur when students are prepared to learn before formal instruction takes place. According to PFL theory, students are prepared to learn a particular concept by working on sets of problems for which the concept provides an obvious solution. The problem sets are designed to give students a kind of organic understanding of the structure and the parameters of concept – the shape of the key, if you will - they will need to open the door to solving the problems.
In the TWD unit, the major concepts to be learned are data literacy, data-based argumentation, and proportional reasoning. Students are prepared to learn proportional reasoning by working on a set of problems in the Social Studies module that are organized around the question of how to equitably share the water in the Tigris/Euphrates watershed. Students are given all the information they need concerning population, water availability, and water use for each country and are asked to develop a treaty among the three countries that fairly divides up the water. Although most students realize that they just can’t divide the water into thirds because the countries have very different populations, they lack the mathematical tools to devise precise answers.
It can be very dificult for Social Studies teachers to leave students without a solution to the issue of fair distribution of water in the Tigris/Euphrates watershed. They should remember that students receive formal instruction in proportional reasoning when they move into the Mathematics module. In the PFL framework, this is called formal learning. In the Mathematics module, students are shown how to create compound measures to represent proportions, per capita and percent in particular, and practice applying proportional reasoning to to solve problems across a variety of contexts.
PFL+
However, the real application of proportional reasoning (in combination with the data literacy and data-based argumentation processes they have also been acquiring) comes in the Science module. And it is here that the TWD approach extends the typical PFL approach to what we call PFL+. PFL reverses the traditional lecture-and-apply process to have students first investigate a complex problem and then learn its canonical solution. In the PFL+ approach we use in the TWD unit, formal modeling in Mathematics becomes the beginning of a PBL-type modeling, scaffolding, and fading sequence as students apply the data literacy and proportional reasoning skills they have learned in Social Studies and Mathematics to solving new problems in Science and communicating their solutions in English Language Arts.
It should also be noted that mini-PFL and PFL+ sequences are employed in many of the lessons across the TWD unit. For example, the three Science lessons centered on data-based explanations are structured around a PFL sequence of exploration, sharing, and telling. Likewise, the first three lessons in the Mathematics module are built around PFL sequences. Similar lessons can be found in Social Studies and English Language Arts. It is important for teachers facilitating these lessons to not only give students time to explore the relevant problems within their small groups, but also to defend their explanations/ arguments, before leading students to correct solutions. Teachers should especially plan plenty of time for groups to present and defend their solutions/explanations to the whole class and encourage and model challenges to these based on the data. Teachers should also be mindful of the place of their modules in the large PFL sequence.
Research Findings
Teachers trying to implement PFL or PFL+ at any level may take comfort in research findings that demonstrate the effectiveness of the PFL approach (Swan et al., 2010). Researchers tested the TWD unit in two suburban middle schools in Northeast Ohio. In each school, one seventh grade team (teachers and students) completed the TWD unit while the rest of the seventh grade teams did not. All seventh graders in both schools were given a five-question data literacy test at the start of school and the same test again in January, after the TWD unit had been completed. Gains in data literacy were compared between groups using repeated measures t-tests. Findings at each school revealed a statistically significant difference between groups, favoring the experimental group (i.e. students who participated in the TWD unit). The effect size of the difference was 1.24 and represented a 20% difference between groups. The chart below compares gain scores for students in TWD (experimental) and regular (control) groups in both schools on each of the five questions on the data literacy test.
As the chart indicates, the greatest differences were found for questions 2 and 4, questions that required data interpretation and synthesis across multiple tables, and data manipulation involving proportional reasoning and calculation. These findings indicate that the TWD materials and their PFL+ approach supported the development of data literacy and proportional reasoning skills among the middle school students participating in the field test.
References
Bransford, J. D. & Schwartz, D. (1999). Rethinking transfer: A simple proposal with multiple implications. In A. Iran-Nejad & P. D. Pearson (Eds.), Review of Research in Education: Vol. 24 (pp. 61-100). Washington, DC: American Educational Research Association.
Swan, K., Vahey, P., Cook, D., van ‘t Hooft, M., Kratcoski, A., Rafanan, K., & Yarnall, L. (2010) Exploring the efficacy of a cross-curricular application of the Preparation for Future Learning framework. Paper presented at the Annual Meeting of the American Educational Research Association, Denver, CO.