# Why Have Students Make and Test Conjectures?

## Because Conjectures Impact Student Learning

**Constructivist theory supports having students make and test conjectures. Constructivism is built on the foundations of Piaget (1950), Ausubel (1960), and Rumelhart (1991) and contends that students construct their own knowledge and are not just passive receivers of information.** Students construct new knowledge based on their past experiences and previously acquired knowledge.

Despite the strength of this theory, there is evidence in the literature that many college instructors still rely heavily on traditional lectures for teaching and assessing student learning *(Macdonald, Manduca, Mogk, & Tewskbury, 2004)*. Finding ways to have students make and test conjectures seems like a promising way to move beyond traditional lectures and help students construct new knowledge.

The process of having students make conjectures about predictable outcomes or data analyses and then testing these conjectures to actual outcomes can impact student learning in the following ways:

- Engaging students in learning as they become invested in learning if their conjectures are correct or not.
- Stimulate students to think and reason statistically.
- Giving students a chance to confront their misconceptions or faulty ideas.
- Helping students construct their own knowledge in a way that leads to deeper understanding and reasoning abilities.

### Engaging students in learning

Recent research *(e.g., Chance, delMas, & Garfield, 2004; Cobb & McClain, 2004; Burtch, 2004)*, suggests that having students make and test conjectures in the statistics classroom can engage students and improve learning. Students become interested in finding out whether or not their predictions are accurate, and are more invested in looking at the results of data analyses.

### Stimulate Statistical Reasoning and Thinking

Asking students to make conjectures about possible outcomes of certain events, or possible results of a data analysis, challenges them to think and reason about data *(Cobb & McClain, 2004)*. For example, asking students to predict which, out of a set of human body measurements, might have normal distributions stimulates their thinking about possible values of variables and how those values might lead to a particular shaped distribution.

### Confronting Misconceptions

Having students make and test conjectures is a way to reveal some prevalaent misconceptions about statistical ideas. For example, *delMas, Garfield, & Chance (1999)* had students make predictions about different sampling distributions, based on population shapes. Students tend to believe that the shape of the sampling distribution will resemble the shape of the population from which the samples are drawn rather than a normal distribution. Having them make this prediction and then test it, with simulation sampling distributions, helps confront this misconception.

### Constructing new Knowledge

Students, in an attempt to make sense of their world, will seek equilibrium. They will take new information and connect it with old information in a way that makes sense to them *(Posner, Hewson, Gertzog, 1982; Davis, 2001)*. If the incoming information fits their scheme they will assimilate it with their current knowledge. If the incoming information does not fit their scheme they will seek a way to accommodate it. This processing of information occurs implicitly and because of this it is not immediately obvious to an instructor when a student is developing misconceptions.

This is why it is important to have students make and test their conjectures overtly. In doing so, students become engaged in activities which reveal their knowledge and misconceptions. Having students compare their conjectures about possible outcomes to actual outcomes gives the student a chance to confront misconceptions and improve the development of their reasoning skills.

This instructional method provides students with a chance to either assimilate or accommodate the new information as well as a chance to develop strong associations between earlier conceptions and the new conceptions -- strengthening their reasoning skills. Through this process, complex learning can take place.