Confer with Students in High School Math for Deeper Learning

Guest post by Emma Chiappetta, Math Instructor and Curriculum Coordinator at Wasatch Academy (Twitter: @emmajchiappetta)

I didn’t give a math test all year. You might think I’m crazy, but math is not all about doing as many multiplication tables as you can in under a minute or completing some mess of a computation. Yes, there are certain hard skills that are needed, and performing calculations is part of the business, but there is so much more.

Students need to understand the context surrounding mathematical skills. They need to identify appropriate scenarios for applying each tool. It’s one thing to be able to do the math; it’s completely another to be able to explain your thinking.

I noticed that some of my students were able to blindly perform calculations but when asked to explain what they were doing, they stared blankly at me.

“I’m finding the standard deviation.”

“Ok, but what does that mean?”

“You plug into this formula….”

On the opposite end of the spectrum, given a data set and a standard deviation, students could tell me exactly what the standard deviation indicated, “The standard deviation is huge! There must be some outliers.” When asked how to calculate it, though, they would consistently fumble with parentheses and square roots.

Which of these students should be given credit for proficiency of the standards? Both have deficiencies and yet both should be celebrated for their accomplishments. I found one-on-one conferencing to be a perfect tool for helping both types of students grow and reach mastery.

Structuring Learning Around Conferences

In my class, learning is structured in a way that enables the students to become really familiar with each standard prior to scheduling a conference with me.

First, I introduce students to the standard. They read it, and often don’t have the vocabulary to understand it yet.

I provide them with a menu of learning opportunities: mini-lessons, videos, text, and guided explorations using technology. Once they have a bigger picture of the concept, they move to phase two - practice.

In math, it is important to practice skills so that they can become automatic. We can only achieve our greatest levels of creativity and problem solving when we have basic tools at our fingertips. If you had to spell check every word that you tried to write, you wouldn’t be able to eloquently get all of your thoughts on the page.

This means that mastering math does require some simple rote practice. Again, I provide students with a variety of options; textbook problems, worksheets, IXL, and Khan Academy. They choose at least one but may supplement others if they need more practice.

In the third step, students apply the concept in an authentic way. In my statistics class, this means, applying it to a data set for a project. In my calculus class, this means looking at how the skill can be used in physics, economics, and even art.

Caption: This string art project helped calculus students see that a curve is really the limit of infinitely many tangent lines.

When the students feel “ready” they schedule a conference with me.

Conferences

In every conference, students are required to answer:

• What is the standard asking you to do?

• What new vocabulary and skills did you need to learn?

• Can you show me an example?

Student notes in preparation for the conference.

As they present, I ask probing questions. Some sample starters are:

• How would that example change if…

• Can you come up with your own example where you’d need to use this?

• What could go wrong?

Here is a specific example from a Statistics conference.

Statistics: My students were exploring a standard related to scatter plots and linear regression. After their initial presentation I asked questions like:

• Can you draw a scatter plot? Make sure to label it with two appropriate variables.

• Describe the scatter plot using the vocabulary you just told me about.

• Estimate and interpret the correlation coefficient for your plot.

• Draw a line of best fit and come up with the equation for it.

• Interpret the slope and intercept of the line of best fit.

• Show me the data you’ve been using for your project. Which variables would be interesting to compare using a scatterplot?

• Use the google sheets to make one and add the line of best fit. Interpret it. What does this actually mean in terms of the variables you chose?

Benefits of Conferences

One of my favorite things about conferring is the serendipitous deep conversations that sometimes arise.

In my statistics class, we were talking about stratified sampling, a method where you separate the population into groups sharing a characteristic (for example, race) and sample a few members of each group. I asked whether or not we should sample equally from each group or proportionally. One student said, “Well, it depends on the story we want the data to tell. If we want to show that police violence is a problem, we might try to get the same number of people from each race category so that minority voices have more weight. If we want to show that police violence is not a problem, we might sample proportionally so that white people are more represented in the overall sample.”

My mind was blown. Clearly, this student had a deep understanding of the concept of stratified sampling but further, he was making connections to one of the enduring understandings for the course - that data is a tool for storytelling.

Conferences are also the ultimate tool for differentiation. With students at the top, I can probe them deeper and deeper. They learn to talk about math and the concepts become clearer for them. It also gives me the opportunity to connect with students who might otherwise get less attention because they don’t need as much support during class.

With students that struggle, I can give them pointed mini-lessons during the conference, send them away with more to think about, and conference with them again once they understand more thoroughly. I can also prompt them with examples to jog their memory. Oftentimes, these students lack confidence at first and are surprised by how much they know when they are prompted with the right questions.

All of my students benefit from the conversations. They always walk away telling me that they understand better at the end of the conference than they did going in. They also take ownership of the material and process it into their long-term memory. Conferences also give them a chance to reflect on their learning and use those reflections to learn better as they begin work on the next standard.

Tips for doing math conferencing right

• Ensure that students know the standards - Read them, identify the vocab, skills, and talk about or provide examples of what it looks like to achieve them.

• Give students the chance to practice the skill - At first, students will think they have mastered the standard right away. They’ll schedule a conference with me and I send them back to their seats with more questions to think about. Over time, they navigate how much practice they need to truly get it.

• You, the teacher, need to know the standards inside and out - I need to be able to ask probing questions for students who leave things out. I need to know exactly what students should explain so that I’ll have confidence that they’ve got it.

• Push students to make connections with the enduring understandings and essential questions for the course. Conferences and conversations are a great way to contextualize the learning more broadly. Students will each have individual connections between the standards and the big ideas. Processing those connections out loud draws creativity from each student.

• End each conference with metacognitive questions. My favorite is: What’s a mistake that you made frequently? How can we come up with a way to avoid making that mistake again?

At the end of the year, I asked my students, “what was the most helpful thing Miss C did for your learning?” Almost every single student said “conferences.” I know my students better than any other year and I truly know what they know. Do you still think I’m crazy for not giving any tests?