Gone Fishing: Science, Proportions, and Probability

Gone Fishing: Science, Proportions, and Probability

Sue Pawula

Summary

CCSS and NCTM promote mathematical practices leading to reasoning and connections of ideas to contexts outside of mathematics.  Students are led through an interactive experience where they record fish sample data on an activity sheet and transform it to a connection between rationalizing ratios based on the proportions they observe and connect that to different population ratios of fish in specific ponds.  Teachers should encourage them to use precise language when describing their rationale for the relationship between the proportions of fish from the sample to what the corresponding pond population possibilities it could be determined to be.  Further discussion should be encouraged in other ways that students could determine correspondence between pond population and sample sizes.  Students discover that it is difficult to determine the probability between two pond samples without additional information.  Important ideas on sampling variability, matching proportions, and how this would be dealt with in a real life situation are discussed as well as other strategies and concerns.  Students are led to understand that they can develop proportional reasoning without making calculations through understanding that the proportions can be correlated through similarity predictions.  Questioning by the teacher can lead to the basic understand of the probability continuum and lead to differentiation of other possibilities, probabilities, and the degree of probability.  Students should further understand how different proportions could affect ability to make choices based on statistical data.  The second activity they participated in was to determine fish population increase due to the research facility’s need to determined the best conditions of increasing fish population and estimation of the current fish population from samplings taken after time has passed.  Once again students use fish samples as a basis for the data collected.  This time they are asked to record only the number of the original fish sample (tagged) and the new (untagged) progeny.   From this they are required to use more advanced proportional reasoning than in the previous activity and will require extra guidance from the teacher as they work on strategies.  When sharing strategies the teacher will need to carefully allow teams with more basic strategies to share first in order for them to not feel insecure as other groups share their more advanced strategies.  Student language will use references to part-to-part and part-to-whole and they will need to be exposed to a whole new range of more advance strategies.  These motivating activities allow students to work through the steps that increase their understanding of ratios, proportions, statistical variability, and fractions.

Reflection

These were excellent, interactive mathematical exercises for students to participate in and see their relevance to the world around them.  The creation of the graphs from which to base their proportional predictions and the discussions that were provoked by them caused students to think on a higher level and share with each other.   This was a scenario for rich use of mathematical language, reasoning, and strategy.  Ratio creation helped student identify some proportional correlations easily but the other more difficult relationships caused brainstorming.  The second exercise brought this activity to a higher plain in that students really had to strive and learn new strategies to apply to be able to develop reasoning for their predictions.  This was a very interesting and really great way to get students talking.

Cochran, J. A. (2014). Gone fishing: Science, proportions, and probability. Mathematics Teaching in the Middle School, 20(1), 16-22.