Thursday, December 29, 2016

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
• Plickers
• Classkick

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?

Saturday, December 17, 2016

#SwDMathChat From Patterns to Algebra (part 3)

I'm continuing to blog about my experiences with using the great ideas from the book From Patterns to Algebra.  In case you missed my first 2 blog posts, you can read the first one here and part 2 here.

So we worked on lesson 4: pattern building with composite rules this week.  The first pattern I showed them was the one on the right below with the yellow diamonds.  They were struggling a bit so I showed them the very first pattern we had worked with a few weeks ago (the one on the left without the yellow diamonds) and asked them what they noticed.  I started to hear some "ah-ha's".

My students are starting to get more flexible with this concept.  I can ask them different questions and they can apply what they know about the pattern rule to answer my questions.  For example, for the first few days, all I asked of them was to come up with the rule and what position 4 would look like.  Then I started asking them to show me position 0, or position 10, or how many tiles will there be in position 8, etc.

A few of my students can draw position 4, but are having a difficult time writing the rule independently; I have to prompt them with questions like "what's staying the same?" or "what's changing in each position?" for every pattern.  I have 8 students in this class and about 5 or 6 can come up with the correct rule and patterns for the positions I ask for fairly easily each day.  My big challenge going forward is to figure out how to help the last 2 or 3 make the connections needed to do this independently.

The last few days I really challenged them - I did not use 2 different colors, making it more difficult  for them to determine the constant.  About half of my students were able to identify it after a few minutes of productive struggle.  I love watching them all really thinking and talking about these patterns!

Here are the patterns we worked on this week:

I'm looking forward to the next lesson in which we work in reverse and I give each student a secret pattern rule and they must build what their positions 1, 2, and 3 look like.  Stay tuned...

Saturday, December 3, 2016

#SwDMathChat From Patterns to Algebra (part 2)

(In case you missed my last post on using the book From Patterns to Algebra, I highly suggest you check it out before you read this post.)

The next 2 lessons in the book were similar to the first 2, but instead of just multiplying, now my students needed to think in 2 steps (can you say "nice connection to two-step equations"?) by first multiplying then adding.  We started with the "Guess My Rule" game as before.  The first day I used the rule  x2+2  as suggested in the book.  I had my students volunteer the random numbers for the input column and I gave them the output numbers one at a time.  After 3 sets of input/output numbers I asked them to try to think of the rule.  Many were stuck.  One student (the same student I mentioned in part 1 as a matter of fact) said "This is hard!" (again). But once she figured it out, she again changed her tune and said "Oh, this is easy!"  Most of my students just needed scaffolding to help them come up with the rule.  I asked them to start by looking at just one pair of numbers - "What can you multiply the input number by so that you get close to but don't go over the output number?  OK, then what do you have to add to get to the output number?  Now see if that rule works for another pair of numbers in the table."  Basically trial and error.  Eventually most of them were able to figure this out.

The next day I started by giving them the first pair of input/output numbers and told them "I can think of 6 different rules for this, can you?"  Loving a challenge, they all set out to work. That same girl I mentioned several times already had 4 correct rules and said she couldn't think of any more. That's when I broke into my rant about perseverance and productive struggle.  With my prompting she went back to work and easily came up the last 2 rules.  After we had all 6 rules written on the board, I added a new pair of inout/output numbers. I asked them "Now which rule is the only rule that works for both sets of numbers?"  A few minutes later most had written down the correct rule on their whiteboards.

The third day we started out the same way with one pair of input/output numbers and me challenging them to find 4 rules.  Once they had figured out the 4 rules, I gave them another input number and asked them to write down the output number using our rule.  This was easy for them now that they had the rule, but then I gave them an output number and asked them to figure out what the input number was.  Wow!  You would have thought I'd asked them to explain Einstein's theory of relativity!  We're in the middle of a unit on two step equations so I hinted at the connection.  Love this!  I love the way they're all engaged and challenged by this and they're starting to see the connections.  At first, one student said "But there's no x!" so I had to explain to her that x represents the unknown number, which in this case is our input number.  I saw the light bulb go on and she quickly wrote and solved the equation.

Next, I think I'll let them take turns being the rule makers as the book suggests.  I didn't do that with the first lesson, but when I let them build their own patterns for each other to solve they really loved that.  It gives them some ownership and, as I firmly believe, if you can teach something it really shows that you understand it.  I plan on using this lesson for another day or two and then moving on to patterns with two steps.  Stay tuned!