Math Practice #5 for Teachers

The other day I was trying to decide which of the many tools in my bag of tricks I wanted to use for a quick formative assessment.  My usual routine is just to have students raise their hands to answer my questions and provide enough wait-time for everyone to think about it, or to have them write their answer on their individual whiteboards.  But no matter how much wait-time I provide, there's either that one student who calls out the answer so everyone else stops thinking, or the student who just waits for someone else to answer so they don't have to.  Over this past summer I read Total Participation Techniques and swore I was going to use some of these strategies to get everyone involved in answering, but I really haven't done a good job with that.

So back to my decision of which tech tool to use - here are my usual go-to choices:

• Nearpod 
• Socrative
• Google Form
• Plickers
• Classkick
• Google Classroom Question

I'm looking for something that is quick and easy, will record everyone's answers for later review, and gives everyone an equal opportunity to provide an answer.  I'm trying to assess how my students are understanding the pattern lessons we've been exploring from the book From Patterns to Algebra.  I want to see if they can explain their thought processes using words, not just drawing or building the next position in the patterns.  I want to see if they can explain how they determine the constant and the multiplier.  This is really important as we are going to move on to patterns where all the tiles are the same color instead of having the constant stand out with a different color.  I want to have a good class discussion afterwards to reveal all understandings and also correct misconceptions.

So, my first option - Nearpod - requires me to set up the presentation and have students sign in.  I can see the results in real time and it does save the data for later.  I can even share out good responses and those that are lacking so we can discuss them as a whole class which I like.

The next option - Socrative - also requires that I set up the questions ahead of time.  Yes, I could use the Quick Question option, but as far as I know (please correct me if I'm wrong) the data isn't saved for later review.

Next up - Google Form - again requires prior setup to use, but it does save the data.  But reviewing the data is awkward when it's short answer questions as I'm planning to use.  Forms are also good for multiple choice because they can be graded with Flubaroo, but this was not this case here.

Next is Plickers - my students love Plickers, but they're only good for multiple choice, so that option is off the table.

Classkick is another option, but I find this is a better option for using the drawing tool to solve problems, not so much for typing responses.  

My last choice is the Google Classroom Question feature.  My students are already signed into Classroom all the time, so that makes it quick to access.  And adding a question on the fly is quick and easy too.  I have a class that I named "Templates" where I add questions that I use over and over again.  So when I want to use one, I click on the "+", chose "Reuse post", and pick the question I want to ask.  I love that I can see how many students have submitted their answers and how many have not.  I also find it easy to review their short answers by simply scrolling through them.  I can also provide feedback to them by means of a private comment if I wanted to do that afterwards.

We talk about students' mathematical habits and the 8 Common Core Standards for Mathematical Practices that we want them to become proficient with.  I realized as I was trying to find the "just- right" tech tool for this formative assessment that I was paralleling Math Practice #5 - "Use appropriate tools strategically":

Mathematically proficient students teachers consider the available tools when solving assessing a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software tech tools for formative assessment such as Nearpod, Socrative, Google Forms, Plickers, Classkick, or Google Classroom Questions. Proficient students teachers are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. ...  They are able to use technological tools to explore assess and deepen analyze their students' understanding of concepts.

As I was going through my options for formative assessment ("consider the available tools"), I was making decisions about each tool's strengths and weaknesses ("recognizing both the insight to be gained and their limitations").

I don't think I've ever put this much thought into choosing a tech tool to use.  Going forward, I think I will always make a more conscious effort to "use appropriate tools strategically".


What do you look for when choosing tech tools for formative assessments?

Make sense and persevere

I teach 8th grade Pre-Algebra in a Special Education resource room.  This year I have been blessed with an amazing group of students!  They all try so hard every day to grasp the concepts I am teaching them.  

This week I was particularly proud of them.  We are coming to the end of our unit on linear equations, and I came up with an activity which would really let them demonstrate their knowledge of linear equations and the flexibility to represent the information in various forms.  I knew it was a very challenging activity, but I had confidence that they would all give it 110% of their effort.  

Before we started, I warned them this was going to be really challenging.  They moaned and groaned.  I explained to them that this activity combines everything they've learned so far in this unit and will really show that they understand linear equations.  I first displayed a similar but blank problem up on the SmartBoard.  I pointed out that there were three forms of equations, a table, a graph, and the slope and x- and y-intercepts that needed to be identified.  I told them to all put their detective caps on because they were going to solve a puzzle.  I was going to give them just 1 piece of information, and they have to fill in every other piece of missing information.  You should have seen their faces!  Looks of panic, disbelief, and total lack of confidence.  

I get really math-geeky and excited at this point.  I explain to them that this is soooo cool because everything interconnects with everything else.  That there is more than one way to figure out each piece of the puzzle.  That there is more than one path to get from start to finish.  They look at me like I've totally lost it!

(Warning: I'm about to ramble!)

So, I put one piece of the puzzle up on the board -- a standard form equation.  I ask them what we can do with this?  What information can we get from the standard form of an equation?  They look at me with blank stares and shrugging shoulders.  I guided them to finding the intercepts.  Then I asked them what the intercepts could do for us?  I started to see some light bulbs go on.  I graphed the line using the intercepts. Then I explained that they could have also transformed the standard form into slope-intercept form first in order to graph it.  Then I asked them what we can get from the graph?  Someone volunteered "the slope!"  So we found the slope (and I reminded them that if we had found the slope-intercept form first, we would already have the slope), and I asked what can we do with the information we have so far?  No responses...  I asked if we could write one of the missing equations?  "Oh yeah!"  So we wrote the slope-intercept form of the equation.  (OK, here I go again with more questions -- I really had to drag it out of them the first time through!)  Can we fill in the table of values yet?  I saw mostly blank stares and shrugging shoulders again.  "Substitution" was my clue to them.  One students remembered that they could substitute the x-values I had provided them into the slope-intercept form of the equation to find y.  So we went through that process, painfully...  Then I erased all the y-values and asked them if they could think of another way to fill in the table without substitution.  No responses.  Which order pair do we already know?  What's the special ordered pair in the table?  "Oh, the y-intercept is the one with the zero for x!"  OK, so how can we fill in the rest of the table if we know this one ordered pair?  Can we use the fact that we already know the 'change in y over the change in x'?  "Oh yeah, we know the slope, so we can use that!"  We finished filling in the table using the slope.  Once we had the table complete, I asked if we could now write the point-slope form.  After we did, I explained that they could have also done that without the table since they had the slope and intercepts already and could have used one of the intercepts for the point in the point-slope form.  Phew!  Finally done!  It was exhausting...

But when we were done filling in all the information in, they said "Can we do another one?"  I was so excited that they wanted to do more!  I thought since they seemed so confused and frustrated by the whole process, that they would never in a million years want more!  But they were so persistent and determined to figure out how to put all the pieces of the puzzle together.  We did a few more "puzzles" where I gave them different pieces of information such as just the completed table of values, or just the graph.  When the class was almost over, they asked if we could do this again tomorrow!

My hope is that learning to be flexible and complete all the missing pieces of the puzzle from any starting point will help them truly understand linear equations.  They really demonstrated Mathematical Practice Standard #1 - Make sense of problems and persevere in solving them. I've never seen them work so hard and I was very proud!