The lesson on finding the best mathematical model to fit the “app download” data went well and was a great way to summarize some of the main functions students have encountered and how those parent functions can be shifted around on the graph.  I did have to shorten some of the parts of the lesson and we weren’t really able to get into analyzing the second table of data (paid app downloads) due to time constraints.

 

As far as UDL components, students were very engaged in a variety of ways.  They easily became involved in our discussion because the data was relevant to them and they could relate to it.  They also loved the puzzle-like nature of figuring out which equation would be the best fit.  They participated well as we went back and forth between whole group discussion, work with their groups of 4, and working in partners as they shared 1 device between two people, and working individually on filling out the information and questions on their activity packet.  It was helpful for them to come up with graphs and equations by hand and then see how appropriate technology can help with these items as well.  Using the sliders on Desmos is especially engaging because students see in real-time exactly how the graph responds as they change to parameters of the equation.

 

This was a great lesson for multiple means of representation because students originally saw the data in a table form and then were able to make a graph to represent the data.  Finally, they could generate an equation to model the data and we could really talk compare the various mathematical ways that one single situation can be represented and how you can find rate of change/growth rates and initial values (y-intercepts) in each of the different forms.

 

In terms of expression, students had different ways to express their ideas and what was going on with this data.  They could discuss their ideas verbally as well as recording information on their packet.  Also, there was not just one simple right answer in this situation.  Students could come up with a variety of equations by hand and using the sliders on Desmos.  These equations should have been relatively close to each other, but will naturally vary a little bit.  Students also could come to different conclusions about which model is the best fit.  It could be argued that either the quadratic or exponential models might be the best models for the data, while the linear model was pretty obviously not going to be the best choice, since the data was curved.

 

 

As a result of UDL training and some ongoing work I have been doing to reshape the projects in this class, I decided to give students more options with what the final presentation could look like.  Since the groups chose different books to study, I really wanted the presentations to be as varied as the texts that were read.  I encouraged students to “teach” the content to the class, as opposed to just presenting a synopsis of the book.  Because of this, the rubric also became very important so students could see what I would be assessing and then they could tailor their presentations accordingly.  I worked on my rubric several different times before it was ready to publish-- making sure it was specific, yet still encouraging creativity and allowing students to take risks.  

 

I have taught this class for the last four years, and for the first time I had a group ask if they could make a 20-minute video that would serve as their presentation.  Reflecting back on UDL, I enthusiastically answered, “Yes!”  However, ironically, they discovered as they got started that the prep time would take too long, since literally everything would have to be finished prior to the night of presentations.  I loved the possibility, but in the end practicality won out for this group.  Options are powerful, but sometimes it is necessary to help students narrow the scope as well if their ideas are possibly too grandiose.  

 

Perhaps the most creative presentation involved an Indiana Jones theme in which two students started discussing how the brain works (cue theme music) and then Indiana Jones came running into the classroom to talk about the need for adventure and intrigue in learning.  The students were given treasure maps and they had to look all over the classroom for clues on how the adolescent brain works.  It was brilliant… and so much fun!

 

Overall, I think that presentations went really well and I always learn so much from what the students are reading and discussing.  Adding some specific UDL components to what I had already created for this project added additional depth and choice for students, and it was very successful!   

 

When we first went to the UDL training, I struggled with what Multiple Means of Representation could look like in a math classroom, since so often there is just one right answer and students have to follow specific steps to get there.  It was powerful for me to see how students in your lesson #2 first worked with the information in table form, then as a graph, and then as an equation.  Not only does this appeal to different types of learners, but by the end of the class period, as an instructor you really know if the students understand the concepts.  (I also really enjoyed seeing how you integrated technology into this lesson as well.)

 

In my limited exposure to UDL, you definitely have demonstrated that you understand the heart of the guidelines and how they can be incorporated into your secondary math classroom!