Assessments

A concept map will be used twice in our Geometry in Nature unit. Students will complete a concept map the first day about what they think the relationships between mathematics and nature are and then on one of the last days to see how their knowledge has changed. It would also be interesting to compare their concept maps to the one we came up with as a group for our unit.

Categorizing grid will be used in the “Tilings and Polygons in Nature” lesson. The students will be learning about rep-tiles (replicating tiles) which are shapes which can be put together with other congruent copies to make a similar shape. We would give the students shapes and ask them to classify them between rep-tiles and non-reptiles. Another option is to have the students classify the shapes into rep-n tiles (n is the number of congruent shapes that make up the similar shape). They would be splitting the shapes into rep-2 tiles, rep-3 tiles, etc. This could be either used as a way to test what they had remembered in the lesson and if they could apply those concepts to any new shapes. The only difficulty is that some shapes can fit into different rep-n tile categories; therefore we would explain this fact. It would be interesting to see which of the categories the students place these types of shapes into.

The minute paper will be used in the “Sequences: Finding Patterns and Writing Explicit Formulas” lesson. It is very easy and time efficient and would help us know what the students got out of the lesson or what they missed. It also forces the students to think critically about what was taught since they have to formulate a question about what they still have to learn. It is a nice way to recap the lesson.

The analytic memo would assess the students best after the “Discovering Fibonacci Numbers in Nature” lesson. With this memo, we can make up a situation involving a research grant to be issued on researching the topic and have the students convince some committee why the subject is worthy. They would have to remember what was taught and how it is applicable to the real world and convince themselves that it is relevant and important.

The lesson “Symmetry and its application to Nature” covers line and rotational symmetry by exploring the properties of each. In wrapping up the lesson, we would have students write a list (focused listing) on each of the symmetries covered. This would test whether students understand the properties of each type of symmetry. We can then go over the lists as a class to make sure the students know the properties of line and rotational symmetry. The students keep the lists for future reference.

The unit is made up of four sections: Tilings and Polygons, Golden Ratio, Symmetry, and Fractals. We intend on giving a cumulative exam at the end of the unit on the concepts covered over the four weeks. The categorizing grid can be used as a revision tool for the exam. It will have the students sort a list of equations, images, terms, etc. into the four categories making up the unit. The students then use this grid to study for the cumulative exam.