#codemaths:Programming math practice for students

//Checking in

I feel like I need to start the first paragraph of every post with a quick paragraph for those who will judge my whole classroom based on one blog post (not that anyone has every voiced judgement but I don't want to give the wrong impression either). As part of any good math classroom I believe there needs to be a balance of conceptual development, investigation and then, in turn, developing mathematical fluency and efficiency. This post will focus on how I am using computers to develop efficient math students, and will not focus on the conceptual development that has taken place prior to students doing this practice work (think textbook problems).

//Learning Cycle, Conversations and Self-Reflection

I have chromebooks in my classroom, two students to each device, which I actually love in promoting math conversations and collaboration. If offered one device for every student I'm not even sure that I'd want it as an option...seriously. I've spent many (seriously, MANY) more hours than I care to admit developing an electronic form of practice for my classroom that works for my situation and I feel like I'm at a new place personally, thus this blog post.
A few years back I was doing the traditional assign homework, quiz the students and look at the data myself. Big Data in education, we all know the drill. I had all kinds of charts and electronic analyzing going on but I was doing all the analysis, not the kids, and it was after the learning cycle was to have been completed. There are actually quite a few blog posts and processes I've written on electronic student data that I'm actually not even doing now in my own classroom now.
I dabbled in writing rubrics for each learning target for my students which I really actually liked but, for the sake of time and curriculum development, that has been pushed to the back-burner and saved for a year when my course content has fewer changes. In class we don't have "homework" but "practice" and as it is electronic there is an unlimited amount available to students at any time, along with help videos that are an option for kids wanting to review where we've been.
We have dedicated class time for practice (example here) and it keeps individual learners at the focus rather than the pace of the whole class. I actually think it's tragic to hear that many 12, 13 and 14 year old kids are having to do 3-5 hours of homework every night before bed rather than spending time with their family and I don't want to be a contributor to that any longer.
I've done the whole clicker thing and what I didn't like with that was there was a lot of down-time and waiting and a lot more focus on the right answer than the process and conversations. Maybe that's because we were gathering data and in education we want it to be "valid" and "formative". No thanks, I'd rather have my kids talking about the math they are wrestling with than getting pure data from them.

Properties of Exponents Review

//codemaths

I've written some about this in the past and wanted to highlight some of the changes I've put together. I'm presenting on this at the NCTM Regional Conference in Minneapolis, Fall of 2015 from both a teacher perspective as well as using it as a tool to challenge students to think more deeply about the math concepts they are learning while applying them in a pseudo-code environment. I tried going full-blown javascript with a class a few years ago and realized so much time is lost in so many of the small details of just writing code that we would never ramp up soon enough to get to applying the math we were currently learning. Today for example in class I found a couple of side-tracked girls that had clicked on the code link from a practice set they were working on and I think I have them hooked on a code challenge to write a system of equations and an algebraic solution based on three randomly generated variables.

//Screen

Kind of a sneaky teacher thing but I have it programmed to go through a subtle gradient of background color (starting at white). If a student continues to get consecutive questions correct their screen will move through shades of green toward blue. As they get consecutive questions wrong it will move through through yellow shades toward red. For a student looking directly at the screen they may not even notice it but as I'm walking around the room it is easier to see and it helps as a visual cue even from across the room for me to go check in with a pair of students if they aren't already calling for help.

//Stars

Far from gamification but after a set number of correct questions, based on quantity and percent correct they can get 1, 2 or 3 stars to show up. It doesn't save to their profile, record it anywhere or even go in as a grade book but it's laughable at how that actually motivates some kids to try harder and not rush through their thinking. Occasionally I'll hack my own code and pictures of my face will show up as they get more questions right. I thought it was funny--some thought it was creepy but deep down I think that means it's awesome so I keep doing it.

//Auto Math Formatting

This has been the latest project with many times where I almost gave up and it turned out I had literally one character in the wrong "else if" loop. I didn't want students to get hung up on understanding what 2x^3 represented mathematically so after the code is printed it will go through and format text (like in in the image above) as 2x³ while also formatting fractions and subscript labels, all based on order of operations so 1/2x will be 
shown differently than 1/(2x) for example. As students type their responses in a text box they will also see a math 
formatted preview of what they are entering.

//Makers

I've tried hard to make this all in a way that can be shared and duplicated but I recognize at this level you really need to have some level of javascript understanding to make something like this work for you. What I've found to be true for me though is that it has become easier for me to make specifically what I need for a lesson rather than trying to find something that is close to what I need. Here's a link to a getting started guide I've put together and I'd appreciate any feedback if there are steps or parts of the process that are confusing. I can't believe you've read this far, you must be pretty nerdy too.

Triangle Inequality: Introducing a learning target in context

In starting a new unit today I wanted to give context to students for writing inequalities. In our algebra class students have not yet learned the triangle inequality theorem which states that:

The sum of any two sides in a triangle must be greater than the third side.

Seems like a great opportunity for some 'ruler math'. I kept the rulers on my desk until after the bell because spring break starts after today and I know how middle schoolers can we with unstructured time and these tools...

In anticipating the pacing to be different for each student I made  the activity as a Google presentation and provided students the link, instructing them to do their work on paper and answer completely any questions asked of them in the activity--noting that I would be breaking in periodically to the whole class and facilitating some discussion.

My favorite part was #4 of the first drawing where many of them grew frustrated with not being able to construct a 1 cm, 2 cm, 5 cm triangle--thinking it was something they were doing wrong. Kind of a fun way to watch them squirm and I know I'm not the first math teacher to have ever done this.

I had some awesome conversations with students while they were working. One student changed what he said mid-sentence. He went from saying

"The two lengths need to be at least the length of the third...The two lengths need to be more than the third length..." 

I asked him why he changed his wording and he explained the difference between the two correctly. Pretty cool--I made sure to highlight that to the class in our whole group time. This kind of mathematics is so much more fun to teach than the traditional "do this, copy me, don't think" style. I overheard the same student above before leaving say to his neighbor

"Math is my hardest class because you can't just memorize stuff and copy it down. You actually have to understand the concepts to do well." 

I told him I will take that as a compliment.

I am not expecting all students to go here but I am hoping that some make some connections to they pythagorean theorem and how it relates to acute and obtuse triangles in the last slide.

I've already made some revisions to the activity since teaching it one period and I wouldn't be surprised if it changed a little more as the day goes on. As always I'm open to other ideas or revisions to make it a better experience for my students.

Desmos' Function Carnival!

Thanks Dan Meyer and Desmos! Start playing #hwdsb math teachers and students!
https://t.co/sfXqNX42wt #storygraphs
— Christine Chan (@chanland) February 7, 2014

I came across Function Carnival on twitter a couple nights ago and instantly knew it was going to be great in class. This is what technology in a math class should look like. We aren't throwing more practice at kids but are instead slowing it down, providing them a tool that creates the conversations more naturally and motivates them to explore the 'what ifs' when factors are changed. Embedded is also a reflection tool that shows students an example of another (fictional) student and asks them what the student is thinking or saying with the graph they have created.

On the teacher side I get a dashboard of every student computer, what graphs they have created and even their short response answers to those reflection questions. I had so many kids today talking about what they saw and wanting to show me their work and how well they did. This is what math education should look like as we begin to acquire more classroom technology. It is not (as I've heard in staff development) having a bin of worksheets available for students that finish the basic stuff early. It is conversations, exploration and connections to potential real life situations.

Student graphs after completion

I don't know much of the background as to how this came about but if it was truly a collaboration between Desmos.com and Dan Meyer I'm very excited for the work to come from that relationship! Thanks so much and looking forward to the future work to come!

#codemaths: Student outlining his approach to coding an algebra solution.

We are up and running in class today. This morning I caught a glitch that caused any use of commas to break the code but that is fixed. I had students working in class on this that were already proficient in solving equations with variables on both sides and understanding the causes for no solutions and infinite solutions.

The task for the group working in #codemaths was this:

Code an equation w/variables on both sides. Try to avoid no solutions and ∞ solutions. https://t.co/irksPBOASt

Before you watch the video keep in mind that these students have had little or no experience up to today in writing computer code.

Unpacking a student example of dividing by a fraction

Today in class students were choosing different practice activities for review for our test tomorrow. One pair of students was working on a worksheet that involved dividing an integer by a fraction. This is a topic we have not reviewed yet but that students have learned in past years. As I looked at his work I knew that I wanted him to explain his process to me. As I listened I knew this was something that I wanted to share. While some of his explanation is now based on procedures I really get the feeling that he has a deeper understanding than a student that is just taught to 'flip and multiply'.

In preparation for looking at it in a future lesson I tried to look at what is happening with the mathematics behind his explanation and what to do when a problem addressed is a little messier.

Comments, suggestions and additional strategies are welcome!

Here is the student's work from when he showed the class:

This is my take on what is happening as the student is moving forward with his procedure:

Go, Go, Google Gadgets...away?

Based on a new direction I've taken in my classroom I've updated one of the graphs that displays in my student response system (WiFli Response). In place of the Student Confidence vs. Time graph I've changed it to be a pie chart of the confidence level of the overall class. The first graph really didn't give any conclusive information I've found in using it the last year.

What could this mean for you?
I've also gone through and updated all the gadgets in the teacher view to be charts rather than gadgets. The reason being is that Google has decided to discontinue gadgets. The upside is that charts look pretty, the downside is any Google spreadsheet you have that uses gadgets will stop displaying your data visually until you go in and update your gadgets to charts.
What's the big deal?
I chose to use gadgets in much of what I do because I liked that they update in real time as new data comes in. In what seems to be a step backward I now need to refresh the webpage every time I want to update information in the charts. Hopefully they plan to have charts update automatically (or perhaps this is a network congestion solution of theirs??) I've left a comment on one of their product forms on the issue if you want to see more information.

Making adjustments and seeing benefits

I have always wrestled in my classroom with doing what is best for kids and learning. Opinion or experimenting sometimes win my favor but in the back of my mind I'm always thinking about what research says is best. That being said I've made some changes in my classroom lately that I think (both by opinion and research) are benefitting my students.

Begin with inquiry where students construct or discover much of what they are learning

In the (recent) past the videos were used to introduce new material and the idea was that we'd go beyond that material when students came to class. The trouble came with when students either didn't watch the videos or worse yet didn't understand them. By introducing the material through video I was also bypassing the opportunity for students to construct their own understanding through inquiry and make meaningful connections.

As a geometry teacher I want my students to understand the hinge theorem because they construct some triangles on paper rather than because they wrote something down what I said in a video--that won't make sense to them and they won't be able to apply it in new situations if they don't understand it.
I'm not throwing out videos, I'm changing the role they play in the learning cycle based on Ramsey Musallam's Explore-Flip-Apply method. Students first explore the concept in our classroom community, after our explore activities are complete they then view video (flip) later on to anchor what they are developing in understanding based on the investigation and then students apply the learned ideas to new situations. This has helped in focusing our class time and giving more meaning for us to scaffold our learning on.

Also during our class time I either begin with a question (often review but not always) or a new seating chart. I take attendance either by missing seats or by who didn't respond to the question. I base the seating chart off of data although the kids don't always know that. Our current seating arrangement places kids who scored better on our last assessment next to those that scored lower.

The intent is to raise the level of conversation for all students as we are doing these community based activities. Students will usually just choose their friends (which they still can on some days) but I want to make sure great math is happening at all groups. 

In some cooperative learning staff development I had years ago we were told never to place the highest achiever next to the lowest achiever (neither would be able to understand each other). With that in consideration, I created a seating chart that relies on recent High, Medium High, Medium Low and Low scores. I have students with highest scores seated next to students with the medium low scores and students with lowest scores positioned next to the medium high scorers and some of each at each table group. I also know which table groups are hot-spots in the room so I make sure to get to those more often as I anticipate they'll have more questions. I generate a chart for each class on a selected assessment and then throw screenshots into a Google presentation so I can access them quickly to either print or use at the start of a class.

For those that use my assessment system you can actually add the seating chart template to your current dashboard by searching and installing my seating chart script that is now available in the script library. It is also included for new users automatically.

My instruction needs to be more focused on learning targets.

I was concerned that by focusing on separate learning targets and objectives students would see the learning as separate modules and not make connections but instead I've been finding the opposite to be true. Because we've been more focused, students have more readily made the connections themselves.

As we begin new ideas, they are grasping them quicker and making connections across ideas that I haven't seen with past years. 

Students begin each unit by looking at a self-assessment rubric written for each specific learning target. They continue to look at the rubric as they are in the learning cycle and write down new dates as they see themselves moving to the next level. Students are taking more ownership in their learning by seeing what it will take to get to a mastery understanding of each learning target.
As a teacher I can anticipate the levels of understanding a student will show as they move through the cycle. This helps them identify their own level using specific indicators in the rubric can help them see where they are in the learning process.

Past practice for me was to just give them the "I can" statement but they didn't really know if they could or couldn't or to what extent. 

In anticipation of some students arriving at mastery sooner than others I'm trying to include a link for many learning targets to an activity that is an extension of the learning. Here's an example of a rubric for an upcoming unit.

No more homework quizzes

I've done away with submitting work answers online for class work that is formative in nature (not for grade). I found students were bypassing learning and just trying to come up with answers. I've been able to attend some staff development by Tim Kanold where he said to give students the solutions to homework for them to work toward in place of students not knowing the answers ahead of time. I have put together class work problems where the expectation focuses more on explaining their understanding and applying of skills from the current learning target and integrated review of targets from the past. 

Solutions are posted online (worked out by me) and also in a printed binder in the classroom and students are encouraged to check these both when they get stuck or when they finish. I said last week: 

"Don't assume that you are awesome and got them all right. You might be awesome, but just double check your solutions before you think that." 

By giving students the solutions they are able to check for their own understanding and I am not spending my time recording more data in my grade book or checking individual homework assignments. I can spend my time as a teacher preparing meaningful activities for what we do while we are together.

Always reflecting on what we do

I believe that I will probably be doing something totally different a year from now or maybe even next month as far as class goes. I will always be looking for methods that will help my students learn math (and life) in more meaningful ways. I believe this is what makes us as teachers better is that constant struggle for how we can be better for our students. If you think there is a better way or I am totally off-base with this approach, please feel free to guide me in the right direction in the comments below. If you just criticize without offering solutions that helps no one.

A money ball approach to cross-country coaching?

If you haven't seen the movie Money Ball, I'd highly recommend it--a great sports movie with statistical connections to baseball. Being a little nerdy, mathematical and newly finding myself as an assistant coach from cross country (running) this fall I've decided to try and apply some of those ideas with our team development. I've used some of what I've learned in Google Docs Forms and Spreadsheets to create an online workout log. Students will register for the site using one Google Form, giving us some important team data to have on hand and automatically including them on a team list in a second form. They will create a screen name in the registration and that will be used to display their results on the team results page. Anytime they workout on their own or with the team they record the distance (if known) and their time along with their screen name in a second Google Form.
There will be leader boards that update on the team website showing who has run the most miles, most amount of time, the fastest mile split on workouts over 3 miles, and the fastest timed mile. Making it a little competitive and hoping to tie in with the social media side of things, we're hoping to grow our team and bring in kids that maybe wouldn't normally join the team. We'll also have a graph that displays their pace history (currently shows the past 10 workout entries).
The minimum y-value on the graph is set for the pace of 1st place at the state meet last year--letting them see what the ultimate goal is for our workouts and where they stand. I'm hoping it will give us some good data as coaches to be able to differentiate our workouts and challenge athletes that haven't made any pace progress recently. I have it finished but don't have any real student data yet--will hopefully post updates on that later.

Update on Flipclass Student Reflection and Assessment Results correlation

I surveyed my students again after completing another unit of study. I gave the same survey at the beginning of the year with less definite results than what have appeared mid-year in the graph below. I have correlated individual components of my classroom structure with actual student assessment results. Students self-reported their study habits and I asked them to only answer "yes" or "no" to individual questions if it was true 100% of the time in this past unit. It appears the most significant indicators of a successful end of the unit assessment are students that watch every video (0.28 correlation) and students that ask for help in class (0.2 correlation).

There are some positive things to note in the negative correlations as well I believe: 

• The lower correlation behaviors are all behaviors that would normally be required in a traditional classroom (doing an entire homework assignment, reading the textbook section, taking notes). I see this as students are now able to do what it is they know they learn best with and abandon strategies that simply do not work for their learning style.
• Outside of class study time reported by students was also low so I believe the flipclass approach is taking a large burden of time off of my students this year and placing the majority of their learning time inside of the classroom (although I wouldn't mind if they started studying more at home).

Thank you to all my loyal readers. Last February when I started blogging I never would have dreamed I'd be sitting at nearly 18,000 views today. Happy Holidays!

Using instant feedback in class.

Instant feedback is only beneficial in the learning process if something is done once a mistake is realized. In  my earlier classroom experiences, students completed an exercise and usually did not find out if they were correct or not until I got around to correcting it or going over the answers in class as a group. By then students had forgotten the thought process that went into the answers they arrived at.
In submitting answers electronically and providing students with instant feedback the thinking can be corrected and extended right there on the spot leaving very little time for the incorrect thought processes to linger. I encourage my students to do homework corrections immediately when they see they have a mistake.
In the last couple weeks I've seen them grow in the reflection process and have been happy to see the improvements students have been making. They are becoming more self-directed in their learning and formally explaining their mistakes and demonstrating their corrected thinking.
Here are some examples of student work in the reflection process.

Student 1

Student 2

Flipped classroom data: Comparing participation in activities to assessment results.

If student reflection on learning is important and I believe the different components of my flipped classroom are important in the learning process I thought it'd be a good opportunity to test the results with some classroom data. 

I asked students some yes or no questions and compared the results to their actual test performance. The results will stimulate some great conversations tomorrow about what is working and what is not. Watching each video I have provided shows a strong correlation with the test results where reading every section in the textbook does not seem to have a positive result (which was a little surprising to me).