Interview Questions for Math Teachers

For Leaders 1 Comment

Interviews are a bit odd and may not work all that well. But, every teacher is going to find themselves in the position of an interviewer or interviewee at some point in their career. Regardless of your role, it is worth taking the time to think about what information you want to learn or communicate during this process.

Before we get to the questions, it is important to think about restrictions. My experience has been that interviews are short, really short. Often, they are scheduled for just 30 minutes, but by the time everyone arrives, finishes the small talk, and actually get to interviewing, there are only 15 to 20 minutes. So, let's limit ourselves to 5 questions. And, let's order the questions with the most crucial ones first. That way if time runs low, you have collected the most important information.[2]It is also important to note that, as the interviewer, there are certain questions you are not allowed to ask. Some of them are straight forward: don't ask how much money a candidate has. Others are less intuitive. Even if it is just polite small talk, you cannot ask a candidate if they have children. The assumption is that any question you ask will be used to determine whether an applicant is hired, so you cannot ask about protected traits, beliefs, et cetera.

Let's get to the questions:

If I visited your classroom for a few minutes every day of the school year, what would I notice? 

Most teaching interviews involve a sample lesson, but this only gives a small window into a teacher's classroom. I want to know the routines and practices that teachers use and build on throughout the year. Do you use number talks once a week? Do you build students' understanding of proof through structured discussions and writing? This questions gets at what a teacher believes is most important for teaching mathematics, but, by asking what you will notice in the classroom, you force the applicant to describe actions and practices not just beliefs.

What is the ideal curriculum for your classroom? How would you use it? And, when you need activities outside of its scope, what resources would you draw from?

Curricula are very powerful in transforming teachers' actions and lessons. I want to know what type of curriculum an applicant prefers because that suggest a great deal about their beliefs. Most, if not all, teachers draw from resources outside of their curriculum. So, I also want to hear that a teacher knows where to find strong tasks.

How do we help students develop a positive mindset about mathematics, particularly problem solving?

Regardless of the course or grade level, I want every math teacher working to strengthen our students' mindsets about mathematics. This does not happen by magic. It takes thought and reflection. I want to hear a candidate connect mindset to different aspects of their teaching, especially feedback.

How do you assess students? What types of feedback do you provide?

Feedback and assessment are incredibly powerful aspects of teachers' practices that impact student learning and confidence. I want any potential candidate to have a well-articulated approach to assessing and providing feedback to students. I also want to hear examples of formative assessment and how those assessments are used to guide future lessons and work.

[Insert Large Scale Content Specific Question Here]?

The details of this question depend on the position the teacher is applying for, but it should give the teacher the opportunity to demonstrate their pedagogical content knowledge (see below) for a big conceptual idea that students in their courses will be wrestling with. I want to see that this candidate knows more than just how to "do the math" covered in a course. I want to hear that they know how to help students make sense of big ideas they will be teaching.

From Ball et al. - (2008) - "Content Knowledge for Teaching : What Makes It Special?"

You might, for example, ask a fifth or sixth grade teacher the following: "5th and 6th grade students spend a significant amount of time studying operations involving fractions and decimals. Still, many find story problems that require these ideas challenging. How do help students become better solvers of story problems involving operations with fractions and decimals?"

Final Thoughts

Those are my go-to interview questions. But, like many, I adjust the questions based on how a candidate responds. When I am the one being interviewed, I am thinking about these questions too. I want to be sure to communicate my beliefs about assessment, curriculum, mindset and feedback even if I am not asked directly.

What questions do you like to ask or be asked? I asked this question on twitter and was reminded of some wonderful questions including:

Homework that Empowers all Learners

Conference, Homework, Homework, NCTM Innov8, Presentations, Teaching Practices and Policy 0 Comments

I am at NCTM Innov8 in St. Louis this week, and today I am presenting on homework. Innov8 is a new conference model with a focus on giving teams of teachers ideas based around a specific theme. This year it is: "Engaging the Struggling Learner."

The format of the conference feels fairly different from other conferences I have been to. For example, my presentation is just 30 minutes long, which is a perfect length for me to share out ideas about how teachers can revamp their homework practices and assignments.

As always, I like to share two things when I present: my slides and a document summarizing my talk. If you can't attend my talk, I suggest that you begin with this document which summarizes everything I am presenting about. You can also check out my slideshow:

Flowcharts for Adding and Subtracting Mixed Numbers

5th, 6th, Algorithms/Models/Strategies, Content, Fractions, Lessons, Uncategorized , 2 Comments

As far as processes go, adding and subtracting mixed numbers is pretty tricky. Any given step is fairly doable, but knowing which steps to apply, and in what order is tough.

I find that my students understand each step independently, but need lots of experience discussing, practicing, and figuring out which step to do when and why. To promote these discussions, I had my students construct flowcharts.

screen-shot-2016-10-17-at-9-12-01-am

Think, for a second, about how different the processes are for these computations:

\(4\tfrac{1}{6}-3\tfrac{3}{4}\)

\(4\tfrac{2}{3}-\tfrac{1}{3}\)

In the first expression, you need to make common denominators, regroup the mixed numbers in some way, subtract the whole numbers, subtract the fractions, possibly regroup again, and simplify. In the second expression you only need to subtract the fractions.

I have found that my students struggle with adding and subtracting mixed numbers because they can't understand when certain steps are needed and when others are not. Trying to teach this through direct-instruction fails for most students. There are just to many if-this-then-this points. Students need to process those ideas on their own, you can't just tell them how and expect them to memorize the procedure.

So, I took this challenge as an opportunity to introduce my students to flowcharts. Flowcharts are a way of displaying algorithms and constructing them requires computational thinking. You must consider what possibilities exist and how your algorithm will process the inputs (problems) you give them. This was hard for kids, but they loved it.[4]I find teachers write, "They loved it!"  or similar a lot in their posts. But, really, there is no way to audit this. It's like a cooking show on TV. The hosts LOVE every dish they make, but they could really be terrible. #DeepThoughts

Each box in the flowchart is a command (ex: Make common denominators.) or a question (ex: Are the denominators the same?). Commands should only have one output while questions should split based on the answer. In the example below you can see that this group began by asking if the inputs were mixed numbers.

I had the students work in pairs on individual whiteboards. They used mini-post-it-notes for the boxes. This was CRUCIAL to their success. They are reworking, rethinking, and revising so often that they need flexible materials.

Groups also developed algorithms of varying degrees of complexity, detail, and sophistication. My goal in designing this lesson was to get the students to think through the different conditions encountered when adding and subtracting mixed numbers. Most groups were still revising and reworking their flowcharts when class ended and that was okay! They did not need a perfect flowchart to achieve the goal of the lesson.

The above group's flowchart lead to my favorite conversation. If you look at the chart, you'll see that they have MANY redundant boxes. Of course, that still works, but part of computation thinking is eliminating redundancy and promoting efficiency. After talking this over, this group scrapped their nearly finished flowchart with the goal of using as few post-it notes as possible!

Other groups, like the one below, had a harder time recognizing unneeded redundancy. They made separate charts for adding and subtracting fractions. Still, this allowed us to have conversations about whether one flowchart could have handled BOTH operations.

In class, we have been discussing different strategies for when the fraction you are subtracting by is larger than the fraction you are subtracting from (ex: \(4\tfrac{1}{6}-3\tfrac{5}{6}\)). Some groups tried to build ALL of those strategies into their flowchart. But other groups realized that the always-convert-to-improper-fractions strategy is easiest to describe in a flowchart. That led to dead-simple flowcharts (see below) and also allowed us to discuss how optimal algorithms for humans and optimal algorithms for computers can vary.

I'd love to use flowcharts again in the future, but you need a certain type of algorithm for flowchart creation to be valuable to students. They are best for describing algorithms with many if-statements or conditional steps. I can imagine factoring quadratics or solving equations might be procedures that would benefit from computational thinking. Maybe you can think of other processes that would benefit from a flowchart. I know geometry courses use something like flowcharts for proofs.

Does anyone out there is flowcharts for other mathematical procedures?

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