Five Ways We Undermine Efforts to Increase Student Achievement
(and what to do about it!)
by Juli Dixon

Blog Post Part 6 of 5

Yes – you read it right, this is post six of a five part series focused on the five potentially (Un)Productive Practices and what to do about them. It is a spin off from an Ignite session I provided at the NCTM annual meeting in April 2018. The Ignite can be found at the NCTM Annual website here: beginning at timestamp 21:40.  However, I did not address this sixth practice during my session. You can only do so much in five minutes with 20 slides…

This sixth potentially unproductive practice has to do with small group instruction. Before I share why I feel the need to include this post, I want you to think about small group mathematics instruction you have observed recently, or possibly even one you facilitated. What came to your mind? You likely pictured a kidney-shaped table with four students all facing the teacher.  The students were probably like-ability. Were the questions posed by the teacher high level or low? I would guess that they were low.

During the professional development I provide, when I ask teachers to imagine small group instruction in mathematics the images they share are similar to what I provided here. This is a problem. What is described here is not best practice, especially when the goal is developing conceptual understanding of mathematics.

What is most concerning is that teachers and coaches are sharing with me more and more that they, or the teachers they support, are being directed to use small group instruction in every lesson every day. This is a problem. We know that the learning goal should influence the structure of the lesson because flexible instructional structures promote mathematical sense making. Yet small group instruction, in the way I just described is being promoted as a blanket requirement.

This is where the practice becomes unproductive. This structure may be valuable for practicing procedures, but it is not appropriate for developing concepts.

So what should take its place? At times, whole-class discussion is a better option, as is the use of concurrent small groups (students simultaneously working in small groups on the same task with the teacher pushing in to the groups as opposed to pulling small groups to the kidney-shaped table). Sometimes, the pulled small group is the best option, even when focusing on conceptual development. However, the small group needs to be re-imagined if your vision was like what I described earlier.

Students should be grouped moderately heterogeneously – not with outliers but with some differences across learners to enhance the discourse. Tasks should be worthwhile and the questions that support them should engage students in reasoning. The time should be used to collect evidence of student learning as well as their gaps in understanding. Those of you who know my work and that of my colleagues with DNA Mathematics know that what I am describing here is applying the TQE Process to the small group. I recorded a short video discussion on this topic. If you are interested in hearing more you can find it toward the bottom of the page at this location:

If you want to explore the topic of small group instruction in mathematics more deeply according to what I discussed here you might find the book that my colleagues Lisa Brooks and Melissa Carli and I just wrote valuable. It will be released July 13, 2018 but it is available for preorder at the site I shared in the last paragraph.

I think this is it, the last part in a five part series on potentially (Un)Productive Practices. However, I think I like blogging. I’ve also been encouraged by your responses. I will continue as long as people find what I share to be of value. I am taking requests for topics. The first request I received was to focus on what to do when students don’t share what we need them to share during instruction. I will blog about that topic here next.

Please tweet your thoughts, comments, ideas on this post, or suggestions for future posts to @thestrokeofluck