Monthly Archives: January 2016

The Gift of Questioning


It was 9 years ago when I heard Lucy West say, that in some cultures, a question is viewed as a gift. This has always stuck with me. Since then I’ve been a little obsessed with questioning. Questioning shows up repeatedly in the 8 teaching practices described in Principles to Actions, as well as being one of the practices itself. We know that it takes time for students to adjust to rigorous lines of questioning around mathematical ideas. I’ve seen it firsthand where, upon being asked a question to elicit thinking, a student immediately changes their answer. Then, when probed further, the student changes their answer again. Students often see a question as a subtle way of an adult saying, “You’re wrong.” So, how do we get away from this? I suppose if we asked students these types of questions more often they would adapt. But, how do we model the fielding of tough questions as teachers, and ultimately learners ourselves? Do we embrace them and ponder them? Or, do we immediately try a different answer, then another, until our questioner is appeased? Here are some of the questions that have been gifts for me and students I’ve worked with in the past.

1) Early in my time as an instructional coach I was describing how we were assessing students and tracking their progress to a colleague. He asked me, “So, what are you doing for the students who don’t get it?” I didn’t have an immediate answer for how we were systematically doing this. Discomfort was the immediate effect. But, I allowed the question to sink in, realizing that if I couldn’t answer that, then there was a problem. This question has led to better processes at our school and today we do have an answer for this question. It’s not perfect, but we are using data consistently to identify students who need more help and getting them that help. This question caused immediate discomfort, but was ultimately a gift.

2) About a year ago, I was trying to decide what to do in a situation. Upon asking a colleague for some advice she asked me three questions: How will you feel about your decision in 10 minutes? In 10 days? In 10 years? She didn’t give me an answer to my question, but instead asked me a series of questions that helped me focus on what was important; a real gift.

3) Last year I got to work with a 4th grade class during a formative assessment on multiplicative comparison. The assessment asked students to compare 30 and 300. One student initially compared the two numbers by saying that 300 was 270 more than 30. I asked her to tell me more about how she had figured this out. She explained, but then said, “This isn’t what you’re looking for, is it?” Apparently, I hadn’t brought my poker face A-game. I reassured her that that is one way you can compare two numbers, but asked her, “Could you compare the numbers with multiplication?” Instead of shutting down, she reflected on how she had compared 3 and 12 in the past with multiplication, and applied this to 30 and 300, successfully telling me that 300 was 10 times greater than 30.

I was excited that a few questions bridged the gap between what this student knew and was in the process of learning. I admire the fact that she was able to reflect on the question in the moment without becoming defensive or shutting down. Even though I presented her with a line of questioning that moved her understanding forward, she presented me with a powerful example of staying calm and persevering in the moment of struggle after a challenging question. This is a practice that I hope to aspire to.

My Favorite Thing

As a K-5 math coach, every day I utilize a variety of resources. However, for the last couple of years one continues to come up as my “favorite.” It’s the Mathematics Formative Assessment System (MFAS) which can be found here. The system consists of tasks for each standard and task-specific rubrics. For each level in the rubric there are:

  • Misconceptions/errors
  • Examples of student work
  • Questions to elicit thinking
  • Instructional implications
  • Videos of the task being implemented (for some levels of the rubric in some tasks)

The system is coded to the Math Florida Standards which varies slightly from the CCSSM, but it’s fairly easy to transcode, with 1.NBT.2 becoming 1.NBT.2.2 (the cluster is included in the Florida coding). Florida also added on some of there own standards and moved some of the MD domain around a bit (a topic for a completely different post), but rather than that the coding is similar.

So, why is this my favorite thing as of late?

1. It’s free, and it’s research tested. There was a field trial that demonstrated the effects of using the system which you can read about here. It was found that use of the system produced significant results in student learning. It’s not often that you find such a robust resource that’s free of charge.

2. The system blurs the line between instruction and assessment. Someone recently asked, “So, is the system used for instruction or for assessment?” to which I responded, “Yes.” In Principles to Actions, NCTM supports the practice of eliciting and using evidence of student thinking, which essentially blurs the lines between instruction and assessment. The MFAS system supports this practice with tasks that could be used as instructional tasks. The rubrics provides support in the work of anticipating student responses, questions that elicit student thinking, and sequencing the order in which student work could be shared during a class discussion (Smith & Stein, 2011). The tasks could also be administered as a more formal assessment, then used to drive small group differentiated instruction.

3. The system supports a growth mindset. The rubrics typically have 3 stages (Getting Started, Making Progress, Got It) or 4 stages (Getting Started, Moving Forward, Almost There, Got It) based on learning progressions. I love the idea that, at the beginning level of the rubric, you’re “getting started” vs. the idea that you just don’t know it. The language in the system assumes that the student possesses knowledge about the topic that can be used to move them forward. As well as promoting a growth mindset, there’s practical support for how to move students forward. I recently got to hear a 4th grade teacher use this language while differentiating instruction for her class. There was a transparency in the language that supported students’ understanding of where they were, and knowing that they were on their way to mastery of the grade level standard being taught.

This year we have focused heavily on the use of MFAS at my school. Our county has the luxury of a 25 minute math intervention block where we’ve been able to do this work. The exciting thing is that with consistent use we’ve begun to see large groups of students move toward proficiency in the standards. Below are links to some MFAS tasks that I’ve used recently, with correlating standards, if you’d like to check them out:

Kindergarten – Which Set Has One More (K.CC.2.4c)

1st Grade – Use Addition to Solve Subtraction (1.OA.2.4)

2nd Grade – Solving Two-Step Word Problems: Marbles in a Bag (2.OA.1.1)

3rd Grade – Rounding to the Nearest Hundred (3.NBT.1.1)

4th Grade – Seven Hundred Seventy Seven (4.NBT.1.1)

5th Grade – Dividing Using an Area Model With Larger Divisors (5.NBT.2.6)





One Good Thing


Over the past week I was on the lookout for a good thing as part of the MTBoS blogging initiative. I’m a K-5 math coach and this is my third year embedded at the same school. I get to see the folks I work with grow over time. Likewise, they’ve seen me grow over the two and a half years I’ve been there. Early in my time there, there’s no way I could have predicted a week like this past one. It was crazy, possibly one of my busiest of the school year. However, the blogging challenge encouraged me to reflect on where I’m at… currently. Although the week was busy, there were multiple instances where authentic dialogue unfolded about our practice as math educators.

  • At a math coaches meeting/training this week we had the opportunity to give and receive specific feedback from fellow instructional coaches regarding how we carefully craft coaching conversations.
  • At a training I facilitated on mathematical discourse a participant hung around after we were “done” to engage in some great conversation around what instructional delivery could look like using a more student-centered approach. I got the opportunity to walk her through a task from the training using John Van de Walle’s before, during, and after model.
  • While working with a teacher at my school we were able to dialogue around the specifics of how we scaffold students to support productive struggle and the question of how much scaffolding is too much. Also, we both acknowledged that it’s hard work, but didn’t let that stop us from moving forward in exploring this practice.
  • Multiple teachers sent me emails (without prompting) sharing their assessment data on a current standard. One included students who were proficient, were approaching proficiency, and were not proficient (and the plan for those students moving forward). Exciting!
  • In multiple planning sessions a grade level team and I were able to work through the math collaboratively using visual models and think through how students will make sense of the tasks for which we were planning.

These are the types of things I envisioned happening when I decided to pursue a role that supports other teachers in the teaching of mathematics. NCTM paints a challenging picture of the principle of professionalism in Principles to Actions, but I feel that this week I got to experience a taste of it in various forms… and that’s a good thing.