Here we see tracking, asking broad questions and having choral responses, as well as assessing with the questions about what is already in their model. The teacher then has the students direct her to the missing parts to fill them in.

The first part of this is tracking and assessing. By checking in with different students, the teacher is ensuring all students are following and misconceptions are corrected. She also ensures that students are understanding the material and helping them make their learning visible. After, she is asking the class an advancing question, seeing if they are following the lesson and can guess where it is going next. Great moment indeed!

I think this is both Tracking and Assessing, since here we see the instructor asking everyone to do this as a class. She is actively getting everyone involved in the process, which allows her to check in with everyone while getting them moving and giving them mnemonics and cues to remember the content.

Here the instructor is assessing student learning since she is asking them to recall the learnings from last class. Starting with a short recap of previous material is a great way to gauge retention and prepare next steps for instruction.

This is one of our most important topics to teach as math teachers. We need to teach students how to set effective and worthwhile goals while learning. They need to know how to monitor their progress as well as how to choose an end point that makes sense for their own level. One student may hit a goal after successfully completing three examples without a mistake, while another may choose to reward themselves for completing a single problem no matter how long it takes or how many mistakes they make. Teaching how to choose relevant and topical learning targets will help our kiddos help themselves!

I feel like this is important for many different types of students, as they may feel more comfortable answering or summarizing their thoughts in a certain medium over another. It's highly possible that they could be encouraged to engage with material they otherwise may have left behind because they can answer in a creative way or have more autonomy over their final goal/project!

This can be so difficult to do with students that are NEP or LEP in the classroom. It really makes you teach from a place of intentionality and think about each thing you do while you are teaching along the way. One thing I have been doing lately is trying to be careful of how fast I speak during a lesson to make sure I am not speaking so fast the students lose me in the process.

I always like to think, "What are we testing them on, and how do we remove unnecessary challenges or blocks?" Am I testing a student's ability to memorize steps to a solution, or do I want to see if they can recognize and apply a pattern? Is it relevant to do 4 increasingly difficult examples, or would it be better to use one more open-ended question with multiple approaches? By targeting these barriers and eliminating them, we help everyone succeed. (And yeah, Mr. A., I DO have a calculator on me everyday.)

This is how we connect to our students and help them through their challenges. By helping them see the value of learning and growing, they will want to work through their troubles and gain new insights into problem solving and application of information. To be frank, I think we all have goals that rely more on developing well-rounded and capable thinkers who engage with critical reasoning more than anything. If my students take anything from my classes, I want it to be the ability to apply a set of logic to a situation and produce a solution. That may be a math problem, a moral dilemma, a life choice, an unexpected circumstance. If they can take anything from me, I just want them to be able to reason and make a decision based on facts and logic. Number skills help, and are useful to acquire along the way, but how many of you solve problems for yourself everyday? I think there is much more we can teach than just content, and getting them excited to develop themselves is part of making it relevant to their world.

This screams to me about something brought up in conversation between Dennis and I and that is, "Bringing their world to the content." We can do all we want to try and bring our content to them, but why do they want to learn if they are engaging with content that feels meaningless? I felt that way sometimes in high school, like I was learning about another endless theorem and postulation made for me in advance and scribbled into the margins of a mass-produced textbook. Essentially, it is imperative we help them see where our learning and skills fit into their world and why it's important to try and engage with their work. If we cannot give them at least that, then what makes them want to take anything away from us? I think by expanding the choice of topics in questioning or other projects, it could help more students to engage with the content. I think of things like having a project replace the unit test and have students choose their own relevant topic. Have them prepare some kind of report in a format of their choice and help them develop skills of their choice in-tandem with your content. Add that 3-point bonus question to have your student make a math meme relating to the unit, build a cool construction and shade it. or write their own problem within certain parameters and solve it. There are a lot of ways that choices can help students bring the content to them and themselves to it in tandem. How else can we design materials or apply our work so we can help more students engage with our content?

In a lot of ways, we have to work with broad tools at an individual scale. For instance, with Illustrative Geometry, we are consistently trying to apply concepts written with very open-ended questions and exploration in mind. Positing this curriculum's humble beginnings in constructions as a pseudo, "geometry art class" where students use tools to make conjectures and pictures out of shapes, it really helps stick for some. For others, I use a more targeted approach and point them toward areas they may have a breakthrough by having them question what they know about the shapes they make and what that tells them. It hopefully helps make the curriculum more personal when I take the different approaches. I wonder what other tactics I can add to that toolkit to help reel in all my learners? One thing I would try is ensuring we had a few copies of things like large print workbooks, or a few copies of the materials in different languages to give multinational learners who are LEP, NEP, or feel more comfortable communicating and learning in their home language.

As someone who consistently does this, it's an important skill to make sure students understand what operation is represented by what symbol. Beyond simply giving the appropriate operation, they should also be aware of what words represent it and how they will visualize it. This is especially important for students learning algebra, as they will be using multiple symbols for some operations like multiplication and division. Beyond just understanding how to do the operations, it is key that they understand how we visually represent some of these concepts to help them use context clues.

We are actually using a problem and doing a basic SCLA in my class right now. We have been focused on a "Math Writing Day" which involves students analyzing a problem then using a rubric to score how well they think the piece is written from a mathematics perspective. They will analyze a problem then write a piece that explains the answer to their problem and articulates their steps with attention to appropriate use of math vocabulary and proper procession of steps. I like that I see this idea being used in practice! It also reaffirms many of the math literacy skills that we read about in Siebert & Draper.