Over the past two days I’ve been reading and rereading chapter 8-9 in my summer book study. Chapter eight discusses how mathematicians connect ideas. From what I see in classrooms, this connection of ideas is often directed by the teacher and involves some type of classroom discussion that helps students construct understanding. Intentionally setting aside time to have math discussions and connect ideas from students is worthwhile. The prime example of Debbie (the teacher) allowing time for Gunther (student) to put the calendar in the shape of a clock was especially a memorable portion of this chapter. That opportunity wouldn’t have occurred if the teacher didn’t take the initiative to intentionally plan to use manipulatives to have students construct their own understanding through a math discussion. Having these student math discussions gives educators feedback in whether students are attempting to make/create connections and whether their overgeneralizing. Creating opportunities for student to make these connections is important.
Chapter nine emphasizes the need for mathematicians to use intuition. I appreciate how the chapter indicates that math is often perceived as a very logical content area. It’s truly not, but the perception still exists. Tracy states in the chapter that she’s come to see “mathematics as a creative art that operatives within a logical structure.” I had to reread this a couple times to let it sink in. I’ve heard it over and over again that someone is “not a math person.” What I find interesting about this is that mathematical intuition is developed. Since it’s developed over time it can change. I tend to tackle this issue quite a bit and address it at the beginning of the school year during Open House. Providing students with opportunities to develop this personal intuition can be a game changer. It’s up to the teacher and school to create memorable experiences for students to develop math intuition. That’s a responsibility that each teacher takes up when they open their classroom doors. By increasing their math intuition, students may also increase their math confidence. Educators need to carefully think about the different math experiences that we provide for our students. Those meaningful experiences aren’t always found in general textbooks.
After reading these two chapters, I started to think of what perceived/real barriers stop teachers from intentionally creating these opportunities.
I think sometimes teachers feel as though they’re required to follow word-for-word the scope-and-sequence that’s provided by a district. This can be the case when a newly adopted text is revealed and teachers are highly encouraged to follow it to a tee. Some texts even tell teachers what to exactly say, what questions to ask, and predicted student responses. I’ve been though many different math text rollouts and this occasionally happens. I see it more at the elementary level though. Having common assessments with a specific timeline that everyone needs to follow can also provide pressure for teachers to fall in line with a particular lesson sequence. Deviating from that sequence may cause issues. I find that there’s a balance between what a district curriculum office deems “non-negotiable” and room for academic freedom within a sequence. I’ve been told in the past that a district text is a resource, but for new teachers it may be more than that. There can be a lot of anxiety, especially if certain parts of your instruction model have to follow a pre-determined sequence and is used for evaluation purposes.
Teachers need to feel comfortable in giving themselves permission to use their own intuition. That may be easier said than done and it depends on your circumstance. Despite good intentions, a published text won’t meet the needs of all of your students. I believe that’s why open source resources are frequently shared within the online teacher community. Supplementing or modifying lessons/questions with resources that match the learning needs of your students happens on a daily basis. Dan’s Ted talk hits on that point.
I believe educators have permission to do this while still meeting a strict scope-and-sequence. Teacher confidence also plays a role with how willing someone is to try resources outside of the textbook. Elementary math teachers need to feel empowered to be able to use resources accordingly without feeling as though it’s going to be detrimental in their evaluation. I think that sometimes teachers don’t exercise their academic freedom to the highest potential because it’s perceived as going against a district’s plan. Having math coaches available and supportive administration is also important in changing this perception
The work that we do is important. Creating mathematical intuition happens through repeated experiences.
Sometimes those experiences are beyond the textbook/worksheet and educators have the ability to make them meaningful. I’ll be keeping this in mind as I prepare for the new school year.