Uniting Geometry and Biology Classification Themes

One of my goals as a math and science teacher who cares deeply about students’ appreciation of both subjects as naturally important and interesting fields of study is to find opportunities to integrate the two in authentic, meaningful ways. Oftentimes, the integration of math and science is simplistic - basic graphing, basic calculation, or something similar. I seek opportunities in my curriculum where on-grade-level math content and on-grade-level science content can support and enhance each other in a truly impactful way. All the better if I can incorporate technology or engineering along the way.

One of my favorite such opportunities that I’ve discovered for my 5th graders involves classification using dichotomous grouping. In 5th grade in Georgia, students learn to classify using this type of thinking in two scenarios:

• The scientific classification of organisms (a 5th grade science standard in Georgia)
• The mathematical classification of polygons (a 5th grade math standard in Common Core aligned states)

Both instances of learning classification involve students learning how experts in each field use observable features to categorize something into groups that are acknowledged across the field. For example:

These names come from making decisions about observable features, and placing the organism or figure into dichotomous groups:

In both cases, the line of thinking and type of classification are the same. There are several important learning outcomes common to both subjects:

1. Experts have devised groupings that are shared across the field for utility and common language
2. An organism or figure has multiple names based on subsequent classifications.
3. While we tend to refer to an organism or figure by its most specific name, it also maintains names based upon all prior groupings (a rectangle is also a parallelogram, quadrilateral, polygon, and 2-dimensional figure, and a kangaroo is also a marsupial, mammal, warm-blooded, vertebrate, animal, and eukaryote).

In both subject areas, the vocabulary to be learned is heavy. Typically, students are presented with a chart like this to help organize it.

In order to add some basic technology and engineering thinking to the mix, I devised a project that students build/program over the course of each unit that has been incredibly productive in helping them a) learn the necessary vocabulary, b) develop the type of thinking, and c) maintain interest in what might otherwise be somewhat boring.

Before I get into anything I have to say about the project, allow me to have a student show you an example.

If you would like to experiment with these students’ projects yourselves to see just how open-ended they are, try thinking of an organism or polygon, then using the student-created tool below to classify it. Simply think of an organism or polygon, click on the title slide, then click on the appropriate answers to the questions on the subsequent slides.

How I incorporate these into the instructional units

The creation of these classification tools takes place over the course of the unit of study, not at the end. The development of the project is intended to be part of the learning process rather than an end-of-unit assessment or capstone project. Consequently, development of the project starts on the very first day of the unit, even while students have very little of the knowledge needed to complete it. While it doesn’t have all the features of project-based learning, it does share many of the principals that separate it from a summative project.

Frequently Asked Questions

When do students work on the projects?

If a typical class period consists of a period of teaching time and a period of student work time, development of these classification tools takes place during student work time. I still teach short, direct lessons explaining the vocabulary and classification steps little by little over the course of the unit, and students spend their working time developing the tool rather than doing more typical “work” activities.

Are these individual or group projects?

My preference is student pairs. I find that having a partner is a good “check and balance” for catching mistakes and misunderstandings, but as groups grow beyond two, there begin to be “too many cooks in the kitchen,” as they say. Typically, some pairs will not work well together, and I’ll offer the opportunity to work alone and check each other’s work if need be.

How do students learn the content needed to create this?

I teach small, direct lessons each day. For instance, for the science project, I start day one with a direct lesson on the Prokaryote and Eukaryote domains. The next day, I’ll teach a direct lesson on how eukaryotes are further classified based on the presence or absence of a cell wall. This continues with a new grouping each day. I also provide students with digital resources to move ahead of my lessons if they’re ready. Some students catch onto this very quickly and race ahead of me, which is wonderful!

How is the project graded?

It isn’t. I do confer with groups, spot check them, provide feedback, and teach the students how to check the quality of their classification tools themselves, but the project isn’t graded. I still create traditional assessments (tests, quizzes) of content and vocabulary to assure that students are mastering the content standards just as I would with any other unit. The development of the project is intended to support student learning, not serve as a summative assessment.

How do the two projects work together?

In my particular situation, the unit on scientific classification comes around September, and the unit on classifying polygons comes around March. As such, we develop the science classification tools several months ahead of the polygon tools. When March rolls around, the creation of the second project:

• Serves as a natural opportunity to review September’s science content
• Reinforces the method of dichotomous classification
• Connects the math and science concepts through a common way of thinking

How does the technology work?

Results

Students love creating these projects. The creativity, independence, engineering thinking, and use of technology for an authentic goal naturally engage them and keep their attention. It is a wonderful activity for the culture of my class!

Nonetheless, the development of these projects is the core of how I expect students to learn the content standards in these units, not an extension or supplement. Consequently, I pay close attention to students’ performance on traditional assessments of these standards.

This year, my science students:

• Scored an average of 92.8% on the Classification Unit Test developed by my school district.
• Scored an average of 86.8% on the animal classification standard during their district semester mid-term
• Scored an average of 93.5% on the plant classification standard during their district semester mid-term
• Scored an average of 98.1% on the animal classification standard during their district semester final
• Scored an average of 92.6% on the plant classification standard during their district semester final

These scores indicate to me that not only are students learning the content at a high level during the unit, but they’re retaining in long-term, as well (no review was done for either the district mid-term or final).

I only taught the math unit using the classification project once before that class was removed from my schedule (I’ve taught the science unit using the project four times). The results were as follows:

• Students scored an average of 93.1% on one of the two polygon classification standards on their district mid-term, but only 54.2% on the other.
• Students scored an averages of 85.7% and 87.2% on the two polygon classification standards on their district final.

Considering that my district considers scores at or above 85% on these tests “distinguished” or “exemplary,” seeing class averages in this range is encouraging evidence that students learned the content standards at high levels. Beyond the test scores, however, students were genuinely engaged with content that they typically found boring previously. So not only did it produce good learning results, it also contributed to a class culture of genuine interest in math and science.