Friday, August 11, 2017

New school, new blog title, new #GuidedMath

I just recently found out I'm being moved from the middle school to the high school. Lots of mixed emotions, but after 7 years in the middle school I'm looking forward to this new chapter and challenge in my career. With that said, I thought my blog needed a new title. Last year my posts had gotten away from the "techy" theme, focusing more on the math, and now with the move to the high school, "Tech Adventures in a Middle School Math Class" just doesn't fit anymore. So welcome to "Adventures in Algebra"!!

I've spent most of my summer, besides teaching summer school, working on setting up guided math workstations. I participated in a book study and slow Twitter chat on Guided Math Workshop with the authors Donna Boucher and Laney Sammons, and many other great math teachers, mainly in the K-5 range, but I guess I'm being somewhat of a pioneer in the secondary level.

In the book study I saw a lot of different ways to set up and run the workstations. I'm sure I'll be tweaking this set up a bit once I see it in action, but so far this is what I'm planning:

Workstation 1 is small group time with me. And when I say "small" I mean SMALL! I have small class sizes to begin with since I teach resource classes. My three groups will be 2-4 students only (homogeneously grouped), so I'm looking forward to using this time to be able to truly differentiate their learning. No more whole group lessons where I lose half the class's attention. Most of my students have attention issues to begin with, so it's really difficult for them to maintain focus in such a large group. Being almost one-to-one with me should really help, and being able to teach them on their level will be so much easier in this homogeneous group setting. All 3 groups will get the same content, just at different levels.

Workstation 2 is where the students will go after meeting with me to do their independent work related to the lesson they just had.

Workstation 3 will be a spiral review station. There are 6 different boxes for them to choose from, each with a theme and at least 4 different tasks. Each task is in a gallon ziplock bag with a task card (on cardstock) that has complete directions, extra copies of the worksheet if they do not want to complete it digitally, and any cards, dice, spinners, etc that are needed for the task. Tasks are activities like games to play with a partner (content related of course!), puzzles, mazes, iPad apps to work on, Versatiles, or the occasional traditional worksheet.

I think my students will enjoy having the freedom to chose what they work on. There will be a worksheet to track what tasks they have completed and I will require them to do the first 2 from each box before continuing on in that box to ensure that they are getting to work in every area. On the task sheet they will also be self-evaluating their understanding of the content to help me find out what they need more assistance with during workshop conference time. Most tasks also have accountability built in -- student will be turning in their work to Google Classroom. Students will open the work in Google Classroom on the iPads where they can annotate on them (this is something I just discovered - on the iPads in Classroom you can annotate, but not on our Chromebooks yet) and turn the work in digitally. Some tasks require them to take a picture of their work and turn the photo into Classroom.

progress tracking sheet
task card
annotate task in Classroom

Workstation 4 is more of a basic skills / number sense station. Students will be working on things like the 4 basic operations, place value, order of operations, rounding, substitution, time, and money - all things that freshmen should know but sadly don't.

Students will rotate through the centers each day. Since I'm now at the high school I have 75 minute blocks every other day instead of the 50 minute blocks I had at the middle school every day. Since I will only see my students every other day I want to make sure I get in a small group lesson with every group each day I see them, and I also want them to be able to get to workstation 2 for the independent work as a follow up to the small group instruction. So I have to work out a schedule where this will be able to happen. I'm thinking that they won't always do workstation 3 and 4 in the same day, it will be one or the other along with the first 2 workstations. I will start class with about 10 minutes of a "Do Now" activity aimed at number sense, then we'll have about 15 minutes per station, and the last 20 minutes will be spent finishing up work and I will have time to conference individually with students as well. I'm sure this will need a lot of adjusting to make it work!

Setting up the workstations has taken a considerable amount of time (and I'm not done yet!). I wanted to be sure they were meaningful activities. I also needed to make sure they could understand what to do fairly independently so they aren't interrupting my small group instruction to ask questions. And I wanted them to have a variety of types of activities so they are not too boring. One other thing I considered is the "reusability" factor (not sure if that's even a word?). I tried to include a few tasks in each box that were unique each time they were used, for instance by using number cards or dice to create the numbers in the problems so that each time they have different problems to work on even if they end up doing the same task twice. My hope is not to have to constantly be creating new tasks throughout the year. I'm hoping the tasks I've set up will take us through most of the school year.

I would love to hear from anyone doing Guided Math Workstations with middle school or high school classes. Please comment below or send me an email and we can compare notes and maybe share some resources too!

Saturday, February 18, 2017

#WUEDT6020 Keeping up with EdTech Efficiently

This is my second blog post for my graduate class WUEDT6020 Emerging Trends in Educational Technology at Wilmington University. 

Keeping up with current trends in EdTech can be overwhelming!  There's so much out there to read, watch, and try.  I think growing my PLN (Professional Learning Network) has really helped me hone in on what I felt was important to me.  (I blogged about my PLN a few years ago too - you can read about it here.)  I've learned through the years to limit who I follow on Twitter so I don't get overloaded.  Some people click the Follow button too freely; I am more selective lately.  I look for Tweeps who are interested in teaching mathematics and also those who are using technology to teach mathematics.  That way I'm sure that what I see in my feed is important to me and I don't get caught up in looking at posts about things that won't help me in my classroom, because that is my primary reason for joining Twitter.

Other tools that I have utilized to keep up with new ideas in EdTech is reading blogs, listening to podcasts, and participating in webinars.  My family thinks I'm a real geek because I spend so much of my free time doing these things, but if that's what I'm passionate about, I don't see a problem with that!

As far as blogs I read, you can find most of them on my blog's side bar - just scroll down to the "Blogs I Read" section.  My inbox is filled every day with alerts to new posts that have been made to the blogs I follow.  Keeping up with all of them can be a little overwhelming too, but I try to squeeze in a little time every day to read a few, and catch up with the rest on the weekends while I eat breakfast.  Not everything that the people I follow blog about is interesting to me, so I have learned to skim and delete them instead of reading the entire post like I used to do to save some more of my limited time.

I have to admit I haven't listened to many podcasts lately.  For quite a while though I would listen every Saturday and Sunday morning while I was in the shower - I know that sounds weird!  Some people like to listen to books on tape while driving, I liked to listen to podcasts while in the shower!  The podcasts I listened to were about using iPads in the classroom, flipped classrooms, the SAMR model, using technology to teach math, using Google apps, etc.  Many podcast would have guest speakers, so if I liked what they had to say, I would follow them on Twitter too.

Webinars are another great way to get professional development and keep up with new trends in EdTech.  Some of the first webinars I participated in were on SimpleK12 - "PD in your PJs" is their motto!  That was another way I learned about using iPads in the classroom.  Since then I've participated in other webinars on topics ranging from Minecraft EDU to building student's number sense to using technology for formative assessments.  What I like about webinars is that even if I can't attend the live webinar, most usually have a link to watch it later when it's more convenient for me.

The bottom line is don't go crazy trying to keep on top of all the new EdTech out there - use your valuable time as efficiently as possible.  Pick and choose what you read, watch, and follow so you're only seeing information that is truly important to you - even if that means unfollowing some people on Twitter or unsubscribing to blogs that you no longer find useful.

Thursday, February 2, 2017

#WUEDT6020 EdTech in Math Class

This is my first blog post for my graduate class WUEDT6020 Emerging Trends in Educational Technology at Wilmington University. 

When my school first started adding technology (i.e. BYOD and iPads) about 4 years ago, some teachers were excited about it, others not so much.  Our administrators encouraged us to use it in our classrooms, provided some PD on it, and modeled using it in our staff meetings.  Eventually most teachers gave it a shot, but our math teachers struggled with how to use it with their curriculum.  Most searched for "math" apps.  After attending various webinars and listening to several podcasts, I realized "math" apps were not going work - I needed to find apps that were able to be used for any concept, not just specifically for practicing math facts, factoring, or solving equations for example.  I needed to find non-content specific, creation-type apps that I could build many of my lessons around.  Apps that could be used throughout the school year with any topic.  Apps that the students became comfortable with and adept with because we used them consistently.  Some of the apps I began using on the iPads were:
Then along came our 1:1 Chromebooks.  Luckily they had touch screens because many of the apps I had used on the iPads also had web-based applications that I could continue to use, and many had drawing features, which work really well for math because students can show their work when solving problems and not just submit their final answers.  Many math teachers complained because a lot of the applications did not have equation editors so adding complex math equations with the necessary symbols was difficult if not impossible.  I have seen much improvement in this area - many more applications have added the ability to write math equations, making them much more user-friendly.

I feel like through the past few years I have really scaled back with the amount of technology I use in my classes.  I used to try out new applications all the time and experiment with my guinea pigs students.  I would like to fall short of saying that I used to use technology just for technology sake, but now I do think more about whether the technology will really make my lesson better and help my students understand concepts better.  Here's a short list of applications we use in my math classes this year:
With the exception of Desmos, the rest are all non-content specific, making it easy to use them for any topic we are currently working on.  Actually, I have used the Desmos Activity Builder card sort for many other concepts besides graphing, so I guess you could consider it non-content specific as well!  As far as Kahoot! goes, I don't use it because it makes a lesson better, I use it because it's a super engaging way to review before a quiz.  Another major player in my classroom is Google Classroom, but I didn't include that in my list because I think of it as more of a learning management system than an application to teach with.  It's what's I include links to in Classroom that is the actual EdTech that I use to enhance student learning.

If you teach math and are looking for ways to integrate technology, I would highly recommend you checking out this short list of applications. I have also blogged about several of them in the past as well.  (Check out my blog archives on the right side bar.) 

What applications do you use in your math classes?  I would love to hear about them!

Friday, January 13, 2017

#SwDMathChat From Patterns to Algebra (part 5)

Inspired by San Diego City Schools Middle Level Mathematics Routine Bank, I started out my school year with Do Nows every day to help build my students' number sense.  I did the number of the day, area models for multiplication of 2 and 3 digit numbers, and mental math strategies.  Then somewhere about mid-November I switched the Do Nows to the Guess My Rule or pattern activities from Ruth Beatty and Cathy Bruce's book From Patterns to Algebra, but feeling sort of guilty thinking I was abandoning my number sense routines.  But the more I thought about it, I realized that these activities are all promoting number sense as well.  My students are always doing some heavy-duty thinking, trying to discover pattern rules and predicting what will happen next, and I see them using some of the strategies they learned earlier in the year.  For my special ed students, these activities are really pushing them to their limits and I'm pleasantly surprised at how well they are doing with all of them.  The very visual and hands-on lessons are perfect for them to make the strong connections they need to move onto the important 8th grade concept of graphing linear equations.  Even though this book wasn't written with the special ed population in mind, it is just what they need to be successful!  (If you haven't read about my earlier adventures with From Patterns to Algebra, please take a look at my 4 previous blog posts!)

This week we continued to work on lessons inspired by this great book.  We started out comparing patterns and finished with beginning our adventures in graphing patterns and rules.  Today I was observed by my supervisor and I think he was pretty impressed with the lesson.  He loved the hands-on aspect and was impressed with my students' ability to answer my challenging questions and make the necessary connections between the rules and the graphs.

We started out the week comparing these 2 patterns to predict which would grow faster and why, even though the first position looked similar.  I had them first identify the rule for each pattern, where they discovered that both patterns had a 5 and a 2.  Then they predicted that pattern B would grow faster because they could see that by position 3 there were definitely more color tiles.  We completed the tables to the right together and noticed that they started out with the same exact number of total tiles, but by position 3 there were many more total tiles in pattern B.  I asked them to see if they could figure out why B grew faster than A even though they both had a 5 and a 2 -- what makes the difference?  They came to a consensus that the reason for the bigger growth was that the multiplier of 5 made the pattern grow faster than the multiplier of 2.

I gave them a few more rules to compare, some with the same constant, and some where the constant with the smaller multiplier was much larger than the other rule's constant, like the one below.  I again asked them to predict which would grow faster, and of course they picked the "x6 + 2" because the multiplier was larger.  We started completing the tables one position at a time and they were surprised that their choice actually got off to a slower start.  We continued the table and eventually saw their choice overtake the other rule to take the lead - they cheered!!  I wanted to make the point that the constant really doesn't matter here - it's all about the multiplier.

The next thing we tackled lead us into my favorite part - we're finally getting to graph the patterns and rules!  As the book outlines, I started them off with patterns with no constants.  I asked them to identify the rule in the pattern (on the left) and think about how we could represent the pattern on a graph.  They really had no idea what I was talking about, so I showed them the graph (on the right).  I reminded them that graphs usually have labels on both axes, so what do we need to add to the y-axis as a label?  One student volunteered that we needed to number it so we could see how many tiles there were.  The biggest difficulty most of my students had with this was remembering to "stack" the tiles one on top of the other like a tower instead of placing them exactly as they were in the patterns.  We discussed why we needed to do this -- so there was a one-to-one correspondence to the numbers on the y-axis.

I love this Post-It graph paper!
Next I paired them up and gave them their supplies:  large Post-It note graph paper, color tiles, rulers and markers.  I had already drawn the axis and position numbers on their graphs for them, but they had to number the y-axis.  I first demonstrated how they had to place their color tiles on the graph lines, not in the spaces between so they lined up with the position numbers on the x-axis.  What we also discovered was the color tiles are just ever-so-slightly smaller than the boxes on the graph paper, so after stacking several tiles, they were not exactly lined up with a line on the graph paper -- we just had to slide each position's stack up slightly to match the next line above it.  Then they needed to draw a dot at the top center of each stack, remove the tiles, and connect the dots with the ruler.  (It's amazing how many students could not draw a straight line with a ruler and how many decided to draw their lines free-hand - ugh!)  Lastly, they labeled each line with its rule.  I had them do this for three different patterns so we could have a discussion about what what different about the 3 lines.  Trying to get them to come up with a word like "steepness" to describe the difference was like pulling teeth!  Then I asked them what it was in the rules that was affecting the steepness.  Most eventually concluded that the larger the multiplier, the steeper the line -- that was a perfect place to finish up that day's lesson.  I felt like they were really making the connection between the rule and the line on the graph - yay!!

Here's one of their patterns built on the graph paper, and the final product on the graph paper (we did not graph the 0 position or discuss the y-intercept this day):

Today, as I mentioned earlier, was the lesson that was observed by my supervisor.  We built on yesterday's work by adding the constants and graphing the 0 position.  We discussed where the constant and multiplier tiles should be placed on the graph and decided that the constant should be at the bottom of the stack/tower so you can more easily see that it is the same at every position.  Then we discussed what part of the rule told us where the trend line would start on the y-axis and they discovered that the constant is what determines that.

After a few examples together on the SmartBoard, I turned them loose with their partners to create their graphs.  Again they had 3 lines to graph, but unlike yesterday where I displayed a pattern on the board which they recreated as stacks on their graph paper, today I just gave them 3 rules (no visuals).  They had to decide what the constant and what the multiplier were and show them with the color tiles.  Then they proceeded to draw and label the trend line for each rule.  Each of the 3 rules had the same constant, so they noticed that all 3 lines started at the same place on the y-axis.  Connections, connections...!!

Here's some of their work from today:


Saturday, January 7, 2017

#SwDMathChat From Patterns to Algebra (part 4)

This is part 4 of my experiences with using the amazing lessons from the book From Patterns to Algebra.  (If you missed the first 3 parts, you can read part 1 here, part 2 here, and part 3 here.)  These hands-on, visual lessons are so beneficial for my special ed students!  They have been really engaged in these activities every day, and I love seeing them challenged, thinking and trying so hard to understand all the connections.  I was doing these activities for a Do Now every day for the past few weeks, but this past week and for the next week or so, we will be working on these for the entire class period.  I'm gearing up to start my linear equations unit, so I want to make sure my students are prepared with the background knowledge and skills they need to be successful with linear equations.

This week, since it had been a while since we worked on the patterns lessons due to my week off before break coupled with the 10-day Christmas break, I started out with just reviewing by using the Guess My Rule, first having them come up with as many rules as they could given just one pair of input and output numbers (2 and 10 in the example below), then giving them a second pair of input-output numbers (6 and 26) to have them decide which is the only rule that works for both pairs of input-output numbers.  Once they determined the correct rule (x4+2), I first gave them another input number (7) and they had to calculate the output, then I switched it up and gave them an output number (18) and they had to figure out what the input number was.  This is always more challenging for them and even though I demonstrated a few weeks ago how to write a two-step equation to find the missing input number, they still mainly rely on guess-and-check.  I tried to point out to them that they can use the input-output pairs they already know to narrow down what numbers to use when they guess-and-check.  For instance, if the output number is 18, that falls between the output numbers of 10 and 26 that we already know, so the input number must also fall between the 2 and 6.  Some students got this strategy, while others didn't.

The next day we did the "secret pattern" lesson from the book.  I gave out slips of paper to each student with a secret rule and they had to create their own patterns with the color tiles and 2-sided chips to go along with the rules they were assigned.  Here are some of their patterns:

(One thing I realized after the fact is that I should cut the position number strips apart so they could spread them out more and line up the position numbers under the actual patterns for each position.)

Once I had checked everyone's patterns to ensure they had set them up correctly, I had them rotate to someone else's pattern to first try to write the rule for the pattern, then build the 4th position in the pattern.

Most of my students have gotten pretty good at finding the rules.  As a class, they have decided that the part of the pattern that is the same in every position is the constant and should be written as the part that is added.  They're really good at drawing the 0 position because they are good at finding that constant.  They find the multiplier by looking at the first position's tiles that are not the constant.  I've demonstrated that once they find the multiplier in the first position (for example, 1 set of 5 red tiles as in the last pattern shown above) sometimes it's easier to see that the second position is 2 sets of 5 red tiles is they make a slight separation between each set of 5 red tiles.  I also try to emphasize that they can use the multiplier and the position number to find out how many red tiles there will be at any other position (and that "total tiles = position number x multiplier + constant").  We've practiced describing what position 12 or 15 or 100 would look like - how many yellow circles and how many red tiles will there be.  They're now good at knowing that there will always be 2 yellow circles at any position and that they really just need to calculate how many red tiles by multiplying the position number I give them by the multiplier they discovered in the first position.

Something that I pointed out after they were all done with writing the rule and building the 4th position is (as the book suggests) that even though some of their rules were the same, their patterns didn't look anything alike.  And we also observed how rules that were opposite, such as x5+3 and x3+5 look different even though they have the same numbers.

Next, going off script a little from the book, I had my students relating the patterns to the tables.  First I gave them a pattern to determine the rule.  I had them write out the equations to find the total tiles in each position ("total tiles = position number x multiplier + constant").  I explained that using an organized list would make it easier, so I reminded them to start off with position 1, then 2, etc.  Next, I gave them a table and had them go through a Guess My Rule exercise.  Finally, I split the screen on the SmartBoard and had them look at the numbers from both activities to see if they saw anything in common.  Some of them spotted the fact that position 1 had a total of 8 tiles and that if the input was 1 the output was 8, so as a class we decided that the input numbers were the same as the position number in the pattern and that the output numbers were the same as the total tiles in the pattern.  Now we have a connection between the patterns and the tables in Guess My Rule.

The next lessons coming up will help get them more prepared for our linear equations unit.  We will be observing how changing the multiplier and keeping the same constant, or changing the constant and keeping the same multiplier effect how our patterns act.  Stay tuned for more updates...

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
  • 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.

Image result for common core math practices

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...