Does Geometry Have Room for Statistics?

Algebra 1


Geometry


Algebra 2


Pre-Calculus (if you get to it)


Statistics or Calculus (if you get to it)


This is the traditional sequence for most high schools in the United States and has been for a very long time. But much has changed in the world over the years since this sequence was established. Data are now being produced in tremendous quantities and people must constantly assess statistical claims being made by businesses, politicians, and the media.


Unfortunately, less than a quarter of students are taking a Statistics class in high school.


How Do We Ensure Every Student Learns Statistics?


Certainly we would like to get more students into a full-year statistics course. We argue that this can be done by educating students early about mathematical pathways and eliminating gatekeeping (do students really need Pre-Calculus to take AP Stats?).


But if we really want every student to learn statistics, we need to find some way to teach it in our required traditional sequence of Algebra 1, Geometry, and Algebra 2. There have been some attempts to sprinkle statistics into these classes (linear regression in Algebra, silly area probability questions in Geometry). Unfortunately, these lessons are often less about statistical thinking and reasoning and more about practicing Algebra and Geometry (finding equations of lines and using area formulas).


Some schools have gone further and tried to implement full units on probability and/or statistics in these classes. The problem with this approach is that these units often feel like an "add on" and are very easy to skip. When the school year gets busy or the teacher gets behind, these are the first units to get axed. Many times these units are saved for the end of the year "if there is time". Additionally, we know that math teachers have not been adequately trained to teach statistics, making it an even easier decision to skip this content.


So what is the solution?


Package All the Statistics Together


Instead of a few lessons on lines of best fit in Algebra 1, then a few probability lessons in Geometry, and then correlation and residuals in Algebra 2, let's make teaching Statistics a priority by putting it all together. This would allow students time and space to do some real statistical thinking—not just analyzing data, but also thinking about how the data are produced and what conclusions can be made based on the data.


But where should we teach it?


Teach it in Geometry Class


Take one month of Geometry class and make it Statistics class.

You’re probably wondering at this point: Geometry is a full-year course. How can we possibly free up a month for Statistics? We know that every addition is a trade-off—there’s something else we can’t teach (or have to teach differently) as a result. Our goal is not to rush through all the Geometry content so we can have room for Statistics. Deep learning takes time and is worth the investment. The goal is to carefully consider what we’re teaching in Geometry and how we choose to uncover those topics.


Ideas for Making Room in Geometry


Here are a few suggestions on how to open some time and space in your Geometry class


1. Omit lessons on constructions and tessellations.

We know this hands-on part of Geometry is fun to do with students, but is it essential?


2. Spend less time on topics covered in the Grade 5-8 Geometry standards.

Many of the topics included in Geometry textbooks are actually covered in middle school and even late elementary school standards. While students may not remember everything from those years, we can focus on deepening and connecting those concepts instead of re-teaching them as if students had never seen them before. For example, instead of spending 4 days teaching how to find the area of various 2-d quadrilaterals, spend one day finding area of quadrilaterals by having students explore how each of those quadrilaterals can essentially be rearranged into a parallelogram.


3. Combine surface area and volume lessons.

Instead of treating each geometric solid as a separate thing requiring its own set of formulas, help students see relationships between these solids. Rich, group-worthy tasks allow students to explore and synthesize many ideas about surface area and volume at the same time, which saves quite a few days in your scope and sequence. Teach this unit as if the topic of study was the 8 Mathematical Practices, and all your teaching resources just happened to be related to surface area and volume. Finding surface area and volume of various geometric solids becomes the method rather than the goal of this unit. This approach emphasizes reasoning, sense-making, and problem solving, rather than information acquisition.


See What it Looks Like


At Math Medic, we carefully curated our Geometry curriculum to allow for a healthy introduction to Statistics. The Statistics unit covers four modules:

1. One-Variable Data Analysis

2. Two Variable Data Analysis

3. Probability

4. Statistical Inference