Archives: Blog

Blog Post Part 2 of 5

Wow – I am blown away by the response to my posted Ignite video! You can view it on the NCTM Annual website (https://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/Past-and-Future/2018-Washington-DC/) beginning at timestamp 21:40. I am also thrilled with the conversations shared on twitter (@thestrokeofluck). I didn’t know what to expect as I am relatively new to blogging, so please keep the feedback coming so I can support you to the extent I am able. I will also share the second installment related to these posts regarding administrators’ six spheres of influence regarding teaching and learning mathematics in a blog hosted by HMH within the next week or so. The first post in that series is posted here: https://www.hmhco.com/blog/an-administrators-6-spheres-of-influence-in-mathematics-teaching-and-learning.

Let’s dig in to the second of Five (Un)Productive Practices.

During the Ignite presentation I said that I wanted to talk about gradual release and then gradually get rid of it. I must admit that what I shared was a bit stronger than I had planned. I guess I got caught up in the momentum of the Ignite session. I was probably still reeling from the outstanding presentations provided by my fellow Igniters. It was very stressful to watch such excellent and entertaining five-minute presentations knowing that I was going to share some ideas that were intended to make people feel uncomfortable – and I only had five minutes to do it in!

So what did I intend to say? I intended to say we need to be critical about our over-use of the classroom structure referred to more commonly as “I do, we do, you do.” This teaching technique is being overused during mathematics instruction and people are realizing it! This is a good thing, but it is not enough. In an effort to hold on to a structure that is no longer appropriate to support all aspects of teaching for rigor, people are responding by saying, “you can enter gradual release at any phase.” I can’t be the only one that finds this to be nonsense…

The entire idea of graduate release of responsibility is to begin with the teacher in control of the sense making by modeling a problem or idea (see Pearson and Gallagher (1983) for the original coining of this term in an article on reading comprehension). The teacher then moves to a more facilitated role by supporting students to engage in the task along with the teacher, in essence, replaying what the teacher has shared. Finally, the teacher relinquishes control so that students can demonstrate their understanding.

Changing the order of gradual release, or entering it at a phase where control is already relinquished is no longer gradual release! You can’t gradually release something you didn’t have at the start! OK, enough exclamation points – but this really gets to me.

With all of that said, I do believe that there is a time and place for gradual release. It is absolutely appropriate for teaching procedures. If your goal is to teach a lesson on long division or polynomial division, I strongly encourage you to model the process first, then provide guided practice as your students use the procedure with you, and finally, allow space for your students to practice the algorithm independently. The implementation of gradual release, without modification, is appropriate for procedural lessons. What about lessons more conceptual in nature? This is where gradual release needs to be replaced, not revised.

My colleagues and I in DNA Mathematics (#DNAmath) developed a lesson delivery structure that is appropriate for use with conceptual lessons. I will introduce it here. However, if you want a more comprehensive exploration, I invite you to check out the Making Sense of Mathematics for Teaching series (https://www.solutiontree.com/products/product-topics/dixon-nolan-adams-mathematics-resources.html).

The Layers of Facilitation describe a lesson structure that is more student-centered than Gradual Release of Responsibility. The goal of this structure is to privilege classroom discourse while maintaining a focus on the learning goal for the lesson. The teacher implements a task through the use of whole-class discussion. The teacher supports students to engage in the task through questioning. Full-class discussion around a problem is followed by students all working on the next problem (or set of problems) in concurrent small groups with the teacher pushing into groups to provide support through questioning and to collected evidence from student responses. Finally, individual accountability is supported as students work on problems on their own to provide evidence of where they are relative to the learning goal for the lesson.

The key here, again, is that the students are doing the sense making and the teacher is supporting them to meet the learning goal through the task that is chosen and the questions that are used to support the implementation of that tasks. As stated in the first post, we can transition our unproductive practices to be productive by keeping the learning goal and student engagement at the foreground of our planning and by critically analyzing our instructional decisions and structures. I am looking forward to continuing this conversation!

Please tweet your thoughts, comments, and ideas on this post to @thestrokeofluck

References:

Pearson, P. D. & Gallagher, M. C. (1983). The instruction of reading comprehension. Contemporary Educational Psychology, 8, 317-344.

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

Blog Post Part 1 of 5

Thank you for the amazing response to the ignite session I provided at the 2018 Annual Meeting of the National Council of Teachers of Mathematics (#NCTMAnnual2018) [to view the Ignite session, go to https://www.nctm.org/Conferences-and-Professional-Development/Annual-Meeting-and-Exposition/Past-and-Future/2018-Washington-DC/ and click on the Ignite video – Juli’s talk begins at 21:40]. Based on the feedback I received I decided to write a series of posts to provide a more in-depth exploration into these unproductive practices and what to do about them. What follows is my first in a series of 5 blog posts I will share here over the next few weeks. Please submit comments, questions, and ideas so that I can work them into my responses for my subsequent posts. I am hoping that we can use these posts as a catalyst for some important dialogue here and on twitter (@thestrokeofluck).

While we are focusing on these unproductive practices here, I am also sharing related posts regarding administrators’ six spheres of influence regarding teaching and learning mathematics in a blog hosted by HMH (https://www.hmhco.com/blog/an-administrators-6-spheres-of-influence-in-mathematics-teaching-and-learning)

I imagine that those of you who were not at the ignite might be curious about these unproductive practices by now. Here is the slide I shared at ignite:

These teaching practices are commonplace and often required by administrators and/or districts. Many of them may have been generated from our colleagues in English language arts (ELA) and might work very well in their content areas, however, upon reflection, you will see that they are often unproductive when applied during mathematics instruction. My goals in this series of blogs are to help you to see why these practices are unproductive and also to assist you in generating a plan for what to do about it.

This post will focus on the first unproductive practice of posting the lesson objective (or essential question) for conceptual lessons. Posting the lesson objective for conceptual lessons at the start of the lesson has the potential to undermine students’ efforts to engage in sense making. What does that mean and what can we do about it?

We need to start by acknowledging that the learning goal should determine the tasks that we use and the questions we choose to support those tasks. If a lesson is conceptual in nature, like making sense of division or understanding what factoring accomplishes, then the ways students interact with the content in those lessons should necessarily be different than with procedural lessons like those focused on long division or polynomial division. The issue here is that if students are told what it is they are supposed to “discover” at the start of the lesson then the students have been robbed of the discovery process, even if that process is highly facilitated. There should be some aspect of discovery in conceptual lessons. This is not necessarily the case with procedural lessons. If a lesson is procedural, it is appropriate and even desirable to post the lesson objective at the start of the lesson (Wiliam, 2011). If lessons are conceptual, the teacher guides students to uncover the lesson objective through guided facilitation with the tasks the teacher chooses and the questions teachers use to support those tasks.

When I share this with teachers I get some push back because of the requirements that teachers must post the essential question or lesson objective a the start of the lesson. My gut tells me to respond by saying that we need to work together to change the rules! My pragmatic side reminds me that we don’t have time for this. We must adjust now and change takes too long. While we work together to change the rules to support student achievement in mathematics, we must also work together to survive and flourish within the system we find ourselves. Here is my response to that need.

Using the Four Queries for the Essential Question is a good start. As with any lesson, our first task is to make sense of the learning goal. If the lesson is conceptually based andthere is a requirement to post the essential question or lesson objective, then a useful practice is to “zoom out” on the essential question. By this I mean to word the question or objective in a way that provides students a general idea of the goal of the lesson while protecting the inquiry that should be inherent in a conceptually based lesson. For example, if the lesson if focused on contrasting sharing into groups and making groups to divide, the posted question could be, “How can I divide in different ways?” By the end of the lesson, the student should be able to describe the difference between sharing and grouping to divide. The key here is that the student does the sense making by the end of the lesson rather than being told by the teacher what to think at the start of the lesson. We can transition our unproductive practices to be productive by keeping the learning goal and student engagement at the foreground of our planning and by critically analyzing our instructional decisions and structures. I am looking forward to continuing this conversation!

Please tweet your thoughts, comments, and ideas on this post to @thestrokeofluck

References:

Wiliam, D. (2011). Embedded Formative Assessment. Bloomington, IN: Solution Tree Press.