The power of Desmos

Last year I posted about how we could replace the ti-83 calculators with Geogebra because of the ability to have multiple screens open and be able to do more regression models.  I am not discrediting Geogebra, but I feel that Desmos has been great because of it’s ability to be used on multiple platforms.  This year Desmos has come out with the ability to also complete these regressions and combine it with the original power of Desmos, manipulating in real time.

Having students able to use Desmos on their phone, a school iPad, or a school computer/laptop has been vital for our investigations as we do not have a one to one ratio of tech to student.  It was also great to hear some of the students say “Oh, so I can do this at home?” Also seeing them use their phone for a productive app has been a good transition from all simple games they like to play instead.

I have not used it for all the regression models, but found that it worked really well with teaching about a line of best fit to the grade 9 academic class.  They were told vaguely to graph a line that best fits the data and then we compared it to the one Desmos created.  The students then created the (correct) rules for applying a line of best fit to any model.  It was a great visual to see that it did not have to pass through the origin, and that it does try to place an equal amount of points above and below the line.

Below I have some samples of what it looks like to have the regression models.  I was able to copy data straight from google sheets which was very efficient and easy instead of typing data.

I have also started using it for investigations with linear relations and so far it has helped students with manipulation of the information and visual representations. It is a learning curve as most are used to having information presented to them and then complete the tasks with their new information.

Linear Regression

Quadratic Regression

Exponential Regression

Video Games and Teaching

I recently spent the weekend finishing off the game the Last of Us for the Playstation 3.  I had been meaning to play it for a while but the fact is I never had the time.  After getting started I instantly got into the story and couldn’t stop thinking of ways to beat a certain level or even strategies to best use my player’s skills in the game play (I even asked my students for some hints as I was getting stuck).  The one thing that stuck out to me as I finished was “How can we compete at school with the stimulation that these games are providing our students?”

As a computer programming teacher I instantly saw the connections that could be made and how we could spin a lesson out of video game design and storytelling, and then go on to create our own games.  Unfortunately as a math teacher I was (and still am) stuck on the idea of how to get students into a subject that is often deemed one of the worst classes.  I often try to being humour into the course and try to connect what we are doing to real-life and even popular media (singing all about the bass when working on power laws), but I want to further inquire about gamifying my classroom.

I feel that with the amount of students that play games (girls as well as boys), we could all benefit from the power of gamifying classrooms.  Games provide that connection to our imagination and provide us with opportunities to try new things without being punished when failure occurs.  Although I strive to make the learning zone in my classroom a fail-safe zone where students feel comfortable in answering questions even without full certainty, it is not the same feeling as with a game.  Due to the fact the lives can come back and that you will not be judged on intelligence, failing in a game is much safer than failing in real life.  I have tried to make “games” that have helped the students get interested in tackling problems and being successful in their own learning, but it is not the same stimulation that a game provides.

I have often thought about making the MAP4C class into a game of life or the SIMS, because they learn about buying a house, saving money, and planning for their future.  I think the trouble lies in the delivery of content such as statistics (two-variable data sets, weighted averages, percentile ranks, etc.), exponent laws and exponential functions, and algebraic models (linear vs. quadratic vs. exponential graphs).  There are the trickier topics that can demotivate students and I want to further explore how to incorporate these into the ideas that we have for personal finance, trigonometry and geometry.  These are the questions that I have for myself and have for my colleagues who are further interested in making the courses more interactive like a game as that can help our students stay focused in this over-stimulated world.

It goes without saying that we will have to face the challenges of motivating students for a long period of time when they are developing shorter attentions spans.  With games, smartphones, and Netflix we are becoming the most boring and least controlled element in the students lives.  It is a difficult (but interesting) challenge although I am unsure of how we are able to compete or even teach the students content that they do not feel is applicable to their lives.  Reaching the students and getting them to see the application of content in their lives is one of the greatest accomplishments but is also the biggest obstacle.  We need to use the lesson of great video games: get them hooked to the story and the tasks at hand and they will want to continue attempting the work for hours (even days).

Teaching A Split Class (in Secondary)

This summer I had the unique task of teaching summer school but my class was a split class.  I had a Grade 12 Advanced Functions group and  a Grade 10 Academic group in a single room.  At the start I was really nervous and feeling slightly overwhelmed at the task at hand.  Worrying that the students would not be working if I wasn’t watching them all the time and trying to think about how I would give each group of students the time that they deserved were the initial thoughts I had.  

The first day felt like a rollercoaster ride, simply because everything seemed to have just happened and I didn’t know how it had all worked out.  That night I made sure that I went on to plan the day out better and to make sure I had structured my day to avoid that feeling again.  Once the structure was set out by myself, the students felt more at ease and higher learning took place for most of the students.  The next week and a half went much better although I know that if I am fortunate enough to do this again next year I will have a better idea of what to do.

 

Some of the big takeaways I found in this experience were:

– both sets of students developed their own routine in the classroom.  Students knew when particular tasks were to be completed and they scheduled their time around it.

– students developed a level of respect for one another within the first day.  When I was teaching one group the other would work quietly and not interrupt.

– Grade 12 students were given the opportunity to re-learn topics they may have not been as comfortable with (like factoring) without having to ask in front of their peers

– Grade 10 students could see the applications of the topics they were learning in the new context (I would also vocalize how the skills from Grade 10 were now considered to be skills they knew by Grade 12).

 

One of the big things I would like to do next time is try to create opportunities for the two groups to work together (have the grade 12’s teach the 10’s a skill, or even have the 10’s talk about what they are doing and work through problem solving).   I was wondering if anyone out there has had this experience and has any ideas on how to make it less of two separate groups and more of one whole group.

Teaching Perseverance

One thing I never thought about in my own schooling and on my teaching placements was teaching students the value of perseverance. It is something I became more aware of when I worked at the college level as a teaching assistant and then again this semester when I started teaching the grade 12 college math course.

I think this post links well with my earlier post on growth mindset because I have been trying to implement the idea of “I can” in my students minds. Today was one of those days where I later realized that the teaching I did was more than just teaching math content. I felt like I was able to teach a bit of perseverance to my students today which positively affected those who put in the effort. I had a couple have those “ahh” moments that we hope to see a lot of our students have.

At the end of the class I made sure to let my students know that we did struggle at the start but when they kept pushing through we made it to solving the problem effectively. Before the start of class today I had a student come to get additional work because they were going home sick. This made me realize that I needed to congratulate my students on their efforts because they needed to know that I appreciated their hard work in a difficult task.

I feel like the two lessons yesterday and today gave them the confidence they required in a task that they usually had difficulty with. I have always strived to create a connection with my class so that they felt comfortable with taking chances, but I am still learning how to motivate them to consistently persevere in math.

Replacing TI 83 with Chrome Apps

In the past unit I taught on graphical models, the course focused on regression modelling using the TI-83 Graphing Calculators.  Having used them myself during my high school education I was initially excited for the chance to use them in my own classroom.  Unfortunately it was short lived when I went to the GAFE Summit and I decided to use the Chromebooks and the app Geogebra.

The first day I brought the Chromebooks into the classroom my students were slightly confused on how a math class could use the same technology they used in English and the Humanities.  I introduced the program, created a help guide with Google Docs that they could access, and walked them through the new piece of technology (while assuring them that I was still a beginning user so we were learning together).  After the class ended a lot of discussions arose about the unfamiliarity of the program and how some wanted to use the graphing calculators even though they did not fully enjoy those either.

After the third time we used the tech students who “mastered” the steps were able to help their classmates who did not fully understand how to produce the various regression models.  To my delight students were more appreciative of the new tool they were provided and even found that their resilience was paying off.  Great discussions in the class began about which model to use based on the situation and the R Squared value.  I will admit I was delighted that this was working well and I began to share my new knowledge to my coworkers.

Students wrote their test and instead of the smiling faces or confident submissions I was expecting I found that students were confused and were very upset about their potential mark.  I spoke to some students after the class to understand why they were not very happy with the way the assessment went and their responses initially shocked me.  “We felt like we could produce the graphs and describe them, but we could not describe a graph that was provided for us”.  I thought through the unit and looked at my plans only to realize that I focused a lot of the lesson on being able to use the tech and not as much time as needed on understanding the outcome.

As a first year teacher I realized that I fell into the bad trap of getting lost in the new tech and unfortunately created students who could follow steps instead of thinkers.  One thing that I think will help me in my next attempt at using this is writing out a pros and cons list and a next steps list.  I also started tracking what points students had difficulty with so I can prepare for these in future classes.

My question to those of you reading it is how do you prepare your students to be clearer thinkers rather than students who follow steps? (and this example above was a college level class that I am looking at helping develop deeper understanding)

When do teachers stop teaching a class?

Yesterday morning I was listening to TSN 1050 sports talk radio and they were talking about how hockey coach Ken Hitchcock was talking about how by the playoff time he was not coaching his team anymore. He was merely there as motivation for his team and was simply saying the same things he did all season to the team.

This instantly made me think about how we as teachers are slowly walking away from continually teaching our students and how we are there to guide them in their learning. The only main difference I see is that we are always teaching our students, we just aren’t doing it in the way that revolves around us preaching to them.

This has been one of my major struggles this teaching block because my students are used to and most comfortable with having a note and then practicing similar questions. Today I even tried to have them lead the lesson with a warm up activity on correlations and linear models. This didn’t work as well as I had hoped but the one aspect that is starting to improve is that my class is willing to work through a question without any guidance to see how they fare with it.

My next challenge with this group is to get their excitement up about the upcoming units. The past unit was a major confidence boost because it was something they have been doing for a few years and they have no mastered it. I want to use that excitement and confidence to motivate them through this unit on graphical models and future units to the end of the semester.

How do you motivate your classes when you have students reluctant about a particular topic due to past experiences?