My new main squeeze (mathematically speaking) - Desmos Activity Builder

Over the last couple of months, I have become more and more familiar with the brilliance of Desmos Activity Builder (found at the bottom left of this linked page).  My students have become quite familiar with activity builder as well.  For the last number of years, I have been deeply appreciative of the good product put out by Desmos.  The online calculator is intuitive and really helps students to grasp the conceptual in a way that allows mathematical procedures to have a firm grounding (supporting the effective mathematics teaching practice 6 as defined within NCTM's Principles to Actions).  The relatively new feature of the activity builder has taken it to an entirely different level.

While I have used it in my college classes to support the understanding of my students, it has also been enjoyable to see my methods students develop their own activity builder lessons.  My great successes within activity builder have centered around student discovery of transformations of functions.  Yesterday, my college algebra students engaged in this activity.  

https://teacher.desmos.com/activitybuilder/custom/562e3e7f9236025b1c09a483

I had students work in groups, primarily pairs on this activity. I did this to allow my students to have discussions about their mathematical assertions.  Using collaborative groupings allows for students to have meaningful mathematical discourse as defined in effective mathematics teaching practice 4 within Principles to Actions.  

As students are engaged in the activity, I can monitor progress through the overview page on the teacher dashboard of activity builder.  I really appreciate this feature because I am able to monitor the ways that students are progressing through the activity.  I don't want speed to be a factor in my instruction, so if a group seems to be rushing through the activity, I know this right away.  I can check in with this group to monitor more closely their needed understanding of the concepts.  

Another of the wonderful aspects of activity builder is that I can check student work easily after the students have completed the activity in class.  At the end of this particular activity, I asked my students to find three different quadratic functions that would match to the curves on my "ugly mug" picture.  This was the creation of one group.

Desmos is also a fertile ground for students to work on appropriate vocabulary within particular contexts.  As I monitor their responses, I can step in and ask probing questions to add a certain level of mathematical specificity to their written assertions in Desmos.  

In short, activity builder has allowed me to create an environment where the sense making is placed firmly on the shoulders of my students.  They are actively engaged in the content as they explore the behavior of functions.  It is a great environment for students to take risks and revise thinking.  

Thank you, Desmos!

My biggest success of the 2014-2015 school year. Big board math.

"Teacher, can I please be board?"

Yes, I did spell "board" correctly.  At the end of this semester's final exam for my Math119 Number Sense course I provided my students with an opportunity to give me some feedback on a variety of strategies/technologies I had implemented.  One of these was the use of three foot by two foot whiteboards for table work.  In short, this was a HUGE success.

I have always been a proponent of getting students to look at the work of others.  However, the ways in which we accomplish this can be varied, both in structure and effectiveness.  In the past, I have had groups work together in ways to communicate a concept or to solve a problem that would only allow the kids to put their work under the document camera or to transcribe all of their work at the board.  Both of these methods were inefficient and had drawbacks in terms of the ability for the entire class to stay engaged in the process.  My math classroom at Concordia has always had small, individual whiteboards for class use.  While these whiteboards were decent for individual work, they didn't work very well at all for collaborative work.  In steps the big whiteboard.

Our local Home Depot sells 32 ft square paneling that works great for whiteboards.  Not only is this paneling inexpensive ($13.97 a sheet), but the wonderful people at Home Depot will cut it to size for you.  Including tax, I was able to spend less than $30 to equip my room with eight three-foot by two- foot boards and four two-foot by two-foot boards.

On one particular day of the semester, I was introducing ideas of operations with fractions.  All of these pre-service teachers had some level of prior knowledge with the concepts covered.  I decided to use the big boards to let them show me (and each other) what they knew.  I intentionally wanted to see if they could recall/describe more than just a blind procedure in respect to the operations.

Here is what the students were prompted to do.

Table Task

1.            How would you describe your given fraction operation to a student?

2.            Where do you think they might get confused?

3.            Can you think of a way to help them deal with the confusion?  How? 

4.            Is there a way to represent your operation with a model/drawing?

 As you can see from the big boards, some were able to make some solid group representations, some were not able to do so.

One of the many wonderful aspects of big board work is that the boards can easily remain visible for the duration of class time.  I noticed students referring to the work of classmates throughout our conversations that day.  My six foot square boards rested nicely within the marker trays.  As you can see, I took pictures of the boards for later use.  I noticed students doing this as well.  I can easily see the use of Padlet.com for easy reference at a later time for students.

By nature, big board work at tables forces the members of a group to lean in to the table to work together on the board.  As I have implemented more big board work, I have heard some wonderful mathematical arguments about what one group member saw as relevant for the group's representation.

This sort of collaboration and cooperation is to be firmly entrenched with the best practices mathematics classroom.  SMP 3 is a bedrock of this sort of activity, as students are encouraged to diagnose the big board work of others.  Students are prompted to ask questions of other students, not the teacher.  In the somewhat new document put out by the National Council of Teachers of Mathematics (NCTM) entitled, "Principles to Actions: Ensuring Mathematical Success for All," a clarion call for mathematics instruction is established for our schools.  In this book, the NCTM writers lay out eight focal points that describe good math teaching.  Two of these focal points are naturally a part of big board work - facilitate meaningful mathematical discourse and elicit and use evidence of student thinking.  In short, big board work (regardless of the content) is fertile ground for the kind of teaching we all should be doing within the math classroom.

I have also made use of the big boards to facilitate discussions on homework at the beginning of class.  As students enter the room, I assign each table one problem from the homework from the previous night.  Sometimes more than one group will work together on a problem from the night before.  While the group is determining how best to represent their answer, I am floating throughout the room checking for completion of individual work from the night before.  When a table is done working out their response on their board, they put it up in a marker tray.  In about five minutes, the room has become a discourse magnet, both at tables and throughout the greater room.  After this brief and efficient amount of time, we can move on to our inquiry/discovery/discussion of the day.

For the twenty-one students who responded to my request for feedback on my teaching strategies throughout the semester, they gave the big boards an average score of 9.2 on a ten point scale.  The next closest strategy/technology was Plickers (I will blog on this at a later time).  It is safe to say that my students enjoyed working together, getting up out of their seats, standing, and talking about the beautiful math.  Good stuff!

These were my initial successes with big board math.  Do you have any ideas on how I could make this even better?  I welcome all thoughts.

A funny thing happened on the way to the chalkboard.

As I sit in my classroom while my Number Sense class is taking their final exam, I find myself reflecting on the changes I have made over the course of the last five years teaching this course.  For most math teachers, we have experienced success as students of mathematics.  While this doesn't necessarily seem to be a very bright or insightful statement.  It is.  Embedded within that idea is that most math teachers were students of mathematics in a procedure-driven classroom environment.  This kind of classroom has a very recognizable format for most.

1. Students enter the room with last night's homework.

2. The first fifteen minutes (or more) are spent on going over the homework problems. These problems of discussion are typically selected by the highest achievers in class, leaving those with deeper misconceptions left to sit back and watch (or not watch).

3. The next 20 to 30 minutes is the teacher explaining a procedure or concept to the best of his or her ability.This often includes the teacher writing his or her notes/examples on the board.  The students are then putting down in their notes exactly what is written of the board.  When the highest achievers have questions about a process or product, the teacher will do another example similar to the first, but with different numbers.

4. Fifteen to 20 minutes are dedicated to doing homework in class that is an additional set of problems just like the examples during the lesson.  When problems diverge in thinking from the examples, these are seen as the really, really hard problems.

Truth be told, this was my teaching style of mathematics for many years.  In fact, the first few iterations of my Number Sense class were much like this.  Any teacher who has taught in this traditional format can relate to the frustration that, "My students got it yesterday when I taught them, but today it is like they have never seen it before."  Sound familiar?  It does to me.  

Over the years, I have used an article in my methods and curriculum class for future teachers of middle school and high school students.  This article is written by Stephen Reinhart and was originally published by the National Council of Teachers of Mathematics.  The article can be found here. In "Never say Anything a kid can say," Reinhart proposes a student-centered classroom where the power of collaboration is king.  While Reinhart wrote this article over a decade ago, the themes and strategies highlighted are still very true in math education.  In fact, the Standards for Mathematical Practices (SMP) within the Common Core State Standards for Mathematics CCSSM), emphasize the very same conversational environment within SMP3.  SMP 3 can be found here. In SMP 3, students are required to construct viable arguments and to critique the reasoning of others.  

This requirement of argument and critique begs a certain question in respect to traditional mathematics instruction.  Is it possible (or at least likely) that students are regularly given the opportunity to construct mathematical arguments that are viable?  Do they critique the reasoning set forth by their classmates?  I would respond to those questions with an emphatic, "NO!"

This brings me back full circle to my Number Sense class.  I used to a "good job" telling my students exactly what I knew about improper fractions and division with decimal squares, but I never gave them the opportunity to discover, inquire, and converse about what they knew.  This has changed completely in my most recent versions of the course.  I always have in mind, "Don't tell them, have them do something to create a group understanding at their tables."

I plan to blog in much more depth about my use of technologies (Nearpod, Plickers, Padlet, Aurasma, Kahoot, Desmos, and others) and other engagement strategies (Big Whiteboards [2 feet by 3 feet boards for tablework], speed dating, and "Let the chalk (not really chalk) do the talk").

So, a funny thing did happen on the way to the chalkboard, because now I am no longer on my way to the chalkboard to be a grand orator of math knowledge.  I want to create an environment where the voice of the student is the predominant voice heard in my room.  Research shows that with the right coaching, kids can thrive in this kind of environment and actually see math as much, much more than notes, blind procedures, and something that they are just not good at.