Master Designer is a great beginning of the year task, because it highlights the following three groupwork behaviors, “Helping students do things for themselves;” “Explain by telling how;” and “Everybody helps.” These groupwork behaviors set a very different tone than “There will be no talking;” You may not work together; “and “I can not help you.” These three groupwork behaviors relate directly to math classes of all kinds. In my class, we want students to be trying math problems on their own, at least at first. We also want students to be able to explain how they solved (or didn’t solve) math problems. We also want students to see their classmates as sources of information and not solely relying on the teachers in the room.
Yesterday, I posted a new 3-act task on the blog. In the tradition of digital mentors like Graham Fletcher, Andrew Stadel, and Dane Ehlert, I will rarely post an activity on the blog that I don’t intend to use in my own class with students. Today, we did Make It Rain.
Here is what my students noticed during Act 1…
There’s a lot of money
There are 20’s, 10’s, 5’s, and 1’s
There are more 20’s than 10’s
And here’s what they wondered…
How much money is there?
Why did it go from greatest to least?
Why was it being spread out?
What kind of bills were in the pile?
How many of each bill is there?
My students are used to analyzing their questions collaboratively. Some of the students noted that we couldn’t answer the “why?” questions without asking the person in the video, who we did not have access to (even though it was me!)
As Magdalene Lampert notes in her book Teaching Problems and the Problems of Teaching, “One reason teaching is a complex practice is that many of the problems a teacher must address to get students to learn happen simultaneously, not one after another (2).”
Teaching is hard.
As Max Ray says in his 2014 NCSM ignite talk, “Teaching isn’t Rocket Science. It’s harder.” Max goes on to say that teachers make a litany of educational decisions on the fly based on deep knowledge of content and their students as learners.
Teaching is hard.
As Ball and Forzani write in The Work of Teaching and the Challenge for Teacher Education, “The work of teaching includes broad cultural competence and relational sensitivity, communication skills, and the combination of rigor and imagination fundamental to effective practice. Skillful teaching requires appropriately using and integrating specific moves and activities in particular cases and contexts, based on knowledge and understanding of one’s pupils and on the application of professional judgment (2009).”
Teaching is hard.
As Jose Vilson relates, “We’ve known for decades that building relationships is a central part of our work, but this has even larger implications when we work with disadvantaged students. The teacher-student relationship has so many subtle nuances across race, gender, and class lines that opening our eyes to these nuances would make us better educators.”
The theme of our spring unit is always financial literacy. As teachers of students with varying degrees of need, strength, and interest this means different things for different groups of students. One of my groups is working on selling tickets for our school play, Alice in Wonderland.
We sell tickets at two price points. An adult ticket costs $10 and a child/student ticket costs $8. This is partly my doing, because having two different prices sometimes allows my students to investigate more interesting mathematical questions. Today was one of those days.
Show-goers are also able to purchase play tickets in one of three ways: cash, check, or online with a credit card. My students record the type of ticket and the method of purchase for each order in a table. Students then represent this information visually using graphs. We will use these tables and graphs later on to reflect on the trends and patterns in the ticket sales to make suggestions to our play directors for future ticket sales initiatives. But that’s the bigger picture and I promised you a snapshot. So here it is.
I realized I had been giving my students too much information. As they recorded the total amounts of cash, checks, and credit, I was also telling them the type of ticket. Today we began our routine of using math to figure out the type of tickets using our knowledge of the ticket prices and total amount of money. I gave them this problem as a warm-up:
This past Friday, I gave an introductory presentation on the educational ramifications of new brain and psychological research, specifically, Carol Dweck’s Mindset. What came out of the discussion during the session, was that our school already does a fairly good job of inherently implementing most of the underlying themes in Dweck’s research.
We write narrative progress reports and our grading system is qualitative not quantitative.
One of the most popular ways to critically describe mathematics education in the United States is “a mile wide and an inch deep.” The TL;DR is that most mathematics education focuses on too broad an array of topics with a lack of emphasis on conceptual understanding and critical thinking.
Demonstrated here is a clear focus on an extremely small amount of topics and the only one investigated in any kind of depth is financial literacy, which admittedly is an extremely important topic for students with disabilities. For students with disabilities to be successful members of their communities they need to be financially literate. But this need should not preclude students with disabilities from exploring other mathematical topics.