2018 Ignite at 21:40 (5 minutes)
Global Math Department (1 hour)
DNA Math (Blog Posts)
Rigor, as it relates to the shifts associated with recent state standards, is often defined as the need to include conceptual understanding, procedural skill, and application in mathematics teaching and learning.dnamath.com
Considering this definition, Juli shares the idea that Conceptual is the why and Procedural is the what and that conceptual should be taught ahead of the procedures. One example she shares that I found helpful was division of fractions. Most of us have been taught flip the second and multiply. But as a kid, I always wondered – Why does this work? And who knew to do this?
Juli uses the context of baking cookies and butter, great illustration. I’ll use the idea of money and coins. 3 divided by 1/4. Okay. Lets use the context, $3, how many quarters (1/4) are in $3? 12 quarters. Let’s try how many quarters are in $4? 16 quarters. And again, how many quarters (1/4) in $5? 20 quarters. Then pause and allow students to notice, share what they see, what’s happening mathematically. THEN we can model the procedure… 3 / (1/4) -> 3 * (4/1) = 12, etc.
The big idea is to allow students to play with some math ideas in a context they can relate to, then bring in the procedure and using their thinking and ideas, help them see the connections.
There are times in Algebra the context is a little hazy for me. But even just looking at big ideas and allowing students the space to notice patterns, describe those patterns and then generalize them with the math is a win. (Sara!) What Juli shares as being possibly Un-Productive is that fact that we soft often neglect the opportunities to help students make these connections. And that is so easy to let go. We can sometimes plan an awesome discovery lesson, but without the end discussion to wrap things together, students will walk away, “HUH?!?” and frustrated.
For me, I see this as intentional planning to include time to help them make those connections. I mentioned in an earlier post – closure to class or a learning task is vital. I set a silent alarm on my fitbit that allows me to wrap up class rather than yelling things to kids as they walk out the door. I do a quick review of their responses, then I begin the next day by addressing the previous days take-a-ways. Its where we take many big ideas, reflect on them and decide what we can take away from it all. I feel like the FALs (MathShell) AND Five Practices (Smith & Stein) were great resources to help me formulate how I do this in the classroom.
For this year – I have a few ideas of how to still accomplish this task.
Simply within the MEET chat window, or within a shared jamboard, allowing students to post sticky notes and type the reflection in there. I can easily schedule a question in gClassroom that will appear toward the end of instructional time. I see flipgrid eventually becoming a great tool as well.
My big “new” thing this year will be the “homework” of watching the instructional video prior to classtime. This prepwork will be followed with WSQ gForm. I will encourage students to have these completed by midnight of the day, which will allow me to grab a quick look at them prior to our classtime online together. I can take their questions and ideas and incorporate them into our WSQ discussion we will have at the beginning of class to ensure everyone is moving in the right direction.
If you are unfamiliar with WSQ – Watch, Summarize, Question – check out Flipping with Kirch blog. Ultimately, I want students to do more with the Questioning, but in the first few weeks, I plan to encourage them to use it as a way to communicate their trouble, need for help or clarification.
Again, Juli’s posts have given me a chance to reflect on my practices and process how exactly/possibly I can modify and continue productive practices in a remote environment.