Thursday, June 26, 2014

5 Practices by Smith and Stein

After finishing Mindset and reflecting on it, I chose to read 5 Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein.

I first wondered if actually naming the 5 Practices would give away the purpose of the book, so I was curious how I would blog about it without doing that.  But after reading it, I know there is SO much more to the book than the names of the 5 here they are:  anticipating, monitoring, selecting, sequencing, and connecting.  The whole purpose of the 5 Practices is to best prepare for teaching mathematical tasks so that we have to make fewer decisions during the lesson where we are less able to make good decisions.

It helps me to look at the 5 Practices in terms of the big picture of lesson planning and teaching.  As most people who read math teacher blogs are familiar with The Three Acts of a Mathematical Story [Task], probably most famously, if not first, presented by Dan Meyer, I will present 5 Practices in terms of the 3 Acts...except I'm going to start before Act 1.


Before any planning can occur, the teacher must "specify a goal that clearly identifies what students are to know and understand about mathematics as a result of their engagement in a particular lesson" (p. 13).  After having a clear goal, then the teacher must select an appropriate task.  A task that can be used to meet the lesson goal while engaging the students with the concepts and that "stimulate students to make connections [that] lead to a different set of opportunities for student thinking" (p. 15).  

This part is going to be a challenge for me, because I have trouble seeing what big ideas can be learned from tasks.  I know that there are a lot of tasks available from the #MTBoS, but selecting ones that are going to best fit my goals is a challenge.

Once a goal and a task have been established, the teacher begins anticipating all the possible solution strategies.  Consider strategies that lead to both correct and incorrect solutions.  Then create good questions to ask students who are using each strategy.  If it is a strategy that might lead to an incorrect solution, questions should be redirecting students down a correct path.  ALL questions should seek to reveal what understanding students have about their strategy.

Once this has been done, a teacher should complete a monitoring chart.  Here is an example I created to match what the book suggested:

I want to add a column for questions.  It will help me remember all those questions I came up with!  Here's a link to my version of the monitoring chart. [Note:  You will likely need to download into Microsoft Word to preserve formatting.]

After you have the monitoring chart completed you are ready to teach the lesson.  So here we go into Act 1!


Nothing new from 5 Practices for this act.  Essentially distribute needed materials, read through task, and ensure all students/groups have an understanding of what they are being asked to do.  Work to hook your students into the task so they can't wait to strategize a way to the solution.


After letting the students get to work, the teacher begins to monitor their progress.  This is where all that hard work of finding as many strategies, creating good questions, and having the monitoring chart ready is going to pay off.

As you move from group to group you have preplanned questions to ask students.  Likely the major change of this act as a result of the 5 Practices is that you will take notes on what strategies students/groups are using.  This will better help you prepare for Act 3 and it is also why the monitoring chart is so helpful.

In between Act 2 and 3, the teacher has to make some decisions.  First, select students to present their strategies.  This can be done effectively and efficiently because you have all the notes in front of you.  You will likely want to select at least one student to present each strategy.  Once you have selected the students, you will need to decide on an appropriate sequencing to best facilitate the discussion you wish to have in Act 3.  There isn't necessarily one sequencing that is best, but you must choose one that will work for you.


It is time to begin the conclusion of the task by drawing the whole class together and start sharing strategies.  During this time the teacher has the important job of connecting student strategies to each other and to the learning goal.  Good implementation of this will change Act 3 from a show-and-tell, to actual mathematical discussion.  This will probably be the most challenging of the 5 Practices for me.  I definitely see it as what will turn tasks from "fun days" into "fun, productive learning days".  I also think that the anticipating I will have done with the strategies will help me to see the connections, which in turn will help me guide my students in making connections as well.


There is always the Final Act of reflecting and modifying for the future.  I think the first time I implement a task this year I will plan to do it a different day in each of my classes.  That way I have time to reflect and improve in between implementations of the task.  And since I teach Algebra four times a day, it won't hold the stress of four possible dud lessons on my first attempt.

I am so excited to try to implement tasks.  I think this book really gave me a way to make them a productive use of class time.  My goal will be to implement at least one task per unit.  And in July I plan to continue to develop my units, learning targets, and I will begin selecting tasks :)  

During the year I plan to create a task binder where I keep a record of the tasks I use, the strategies we find, my monitoring sheets, and other notes.  This will help me to stay accountable and to have evidence of what I have done throughout the year.  

One more thought...the book gave a flow chart for The Thinking Through a Lesson Protocol.  I plan to use this as I plan each task, but I will likely modify it to make it more usable to me in my lesson planning.  Don't worry, I'll post again as I plan my first task!



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