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In my school, students are expected to make note by using Cornell note taking system.

Note-taking is good for students to track key information in a lesson, for their revision after lesson, and reflect on  a regular basis.

students need to be instructed and checked on a regular bsais about how to use the note-taking system properly.

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Collaboration is happening om a very frequent basis in my lessns which is deemed very important for students to develop their indepent learning abilities.
Students learn through their team working, debating and coming up with a solution.

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I have a few questions about this that you all might be able to help me with.

Naturally there are certain connections to the local context that may or may not be safe for me to draw - depending on what country I'm in etc. I can avoid those and refer instead to historical examples, no problems there.

But what about mathematics that are hard to draw connections with using the mathematics that we know/teach? For example, complex numbers are super useful but the mathematics required to use them, say, with alternating currents and quantum mechanics are beyond the scope of the class. My take is you can still connect them to other mathematics and connect them historically speaking?

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I need to productively engage students for 100% of the class time using:

Do Nows

Exit Tickets

Interactive/guided notes when lecturing

Keeping lectures short

Maximizing time for students to work on investigations, problems, and quizzes (individually and/or collaboratively)

Use a healthy combination of challenging tasks, simple tasks, as well as low-floor high-ceiling tasks

By engaging students for the whole class and keeping my lectures short, I maximize the amount of time I have to circulate and pay individual attention to students. Individual attention is the best way I know to differentiate.

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Informed by Assessment - Variations on Exit Tickets and "Do Nows"

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Informed by Assessment - Variations on Exit Tickets and "Do Nows"

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Like Mine, and Olga, I also use exit tickets but I do a variation on them. I have students use one index card twice: at the beginning as a "Do Now" and at the end of the class as an "Exit Ticket".  They inform me after the class ends but they also inform students as the class begins and at the end of class.

- I sometimes have students write down a daily achievement goal on one side of the index card as a "Do Now" in the beginning of class. This goal gets reflect upon at the end of class as the "exit ticket".
- Some days I want to just get straight to the content so on one side is a problem for students to solve for the "Do Now" and on the other side students solve another problem for their exit ticket. A variation of this exit ticket problem may become the next day's "Do Now".
- My students have the option to keep their exit tickets if they think they need to review or if they are not comfortable sharing. I lose out on that particular data point but I get a new variable: the number of exit tickets I receive that as a proxy for how confident students are about the day's material.

Two additional things I want to try:
- Sometimes a feelings-check is helpful for students to practice mindfulness so one one side of the index card I might ask questions for students to answer that help them recognize and process their feelings as they come into class as the "Do Now". For example: How are you feeling today and how do you think it will affect your learning? At the end of class they can reflect on that for their exit ticket.
- I also want to make sure that there's a content component to every "Do Now" and exit ticket in the future. So even if I do a feelings-check, I should also be checking for understanding of the content material.

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Basing the lessons on inquiry, develops new skills and furthermore helps students to make connections with the course itself and other courses like Economics, Physics etc. I watched the video named "Inquiry based and conceptually focused mathematics teaching", and there the teacher lead the students to an activity about rate of change. Students have the similar topic in Physics also, so this can be considered as a interdisciplinary activity.

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Assessment plays an important role in learning. I like using exit tickets. I want to see what my students can learn and convert this knowledge during class hours. It is of course important to study after school hours. But I believe that a great part of learning takes place at classroom. This kind of evaluation does not only help students to check themselves but also it gives opportunity to the teacher to check her methods.

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Working together definitely motivates students. But here in this case, it is very important to group the students considering their skills. Each group should be balanced. This type of work sometimes awakens students who don't have that starting activation energy. Once the group members start to communicate and share ideas, it is certain that they will end up with great ideas.

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I use assessment to inform me about the progress of my student and if they need more support in certain areas.
While big tests do not happen very often, I use a lot of questioning and mini plenaries, where I try to give my students a chance to talk through what they have learned.
I like using quizizz for a quick snapshot of understanding of the new concepts.
I also find the exit tickets useful and informative, so that I know what I need to address in the next lesson.

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Differentiation to meet the needs of all learners.
So important! I am lucky at the moment to teach a small class and I can always keep an eye on who needs to be supported in a different way. I think we should be aware about different learning needs of our students so that we help them to achieve their potential.

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I think there are two ways we can interpret this approach.
I find collaboration with other teachers very motivating and reassuring. Not only it gives me fresh ideas and lets me share mine, but also it gives me a feeling of being part of a bigger picture and that I have got support of my colleagues.
But also I think it is important to work as a team with my students. Because not only we are on one side, we all are learning together and I really enjoy noticing unusual solutions and discoveries from my students I would have not thought of.