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I frequently assess my students. If find distinguishing between the more serious tests and those that are solely for the students' benefits helps reduce stress and anxiety on testing. I like to ask a random question at the end of each week/fortnight to show the level of exam questions and how topics are interlinked, not often seen within every lesson. This also gives me more time to go back to weaker topics and identify the strengths of individuals.

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Nayen - Conceptual understanding in mathematics

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Nayen - Conceptual understanding in mathematics

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This is often at the heart of each major topic and must be embedded into their learning. A prime example of this is understanding how chords can be used to get better approximations to the gradient of a curve, leading to the lim h->0 notation used in first principles. If the reasoning and origin are not shown then this becomes another technique, if it is shown and modelled effectively, students pick up better communication skills and are more confident in re-applying the technique and students truly understand its use.

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To promote mathematics naturally lessons must encourage discovery learning. I find planning a lesson around a few examples/problems leads to more natural discussion than planning exactly what you want to say. This is especially important when introducing new concepts, students should be encouraged to ask as many questions as possible even if it leads off topic as you may lead students to making links to different topics and uncovering alternate strategies to tackling problems. I find that this sticks better than going through numerous examples in a row.

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Group work shows that students can improve their critical thinking and problem-solving skills. Furthermore, their way of expressing themselves becomes better. This method helps students learn interactively and efficiently. Activities like that allow them to work and collaborate together to learn and grow from each other. Collaborative learning not only develops higher-level thinking skills in students but boosts their confidence and self-esteem as well.

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It is more than knowing discrete facts and theorem. It is understanding ideas of mathematics. Successful students have the ability to transfer their knowledge into new situations and apply it to new contexts. It helps students and teachers alike to develop a deep understanding of how the concepts inter-relate with each other and build an exemplar that will empower them throughout their education and career.

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Inquiry-based learning promotes engagement, curiosity, and experimentation. Rather than being “instructed to”, students are empowered to explore subjects by asking questions and finding or creating solutions. We must encourage students to ask questions and support them through the investigation process, understanding when to begin and how to structure an inquiry activity.

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Maggie- Teaching through Inquiry (Experiential learning)

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Maggie- Teaching through Inquiry (Experiential learning)

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Ewa - Meeting the needs of all learners and mathematics.

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Ewa - Meeting the needs of all learners and mathematics.

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Students have different learning styles and that is why as a teacher we should try to differentiate our methods. I think I will try more focus on visualizations, especially when it comes to more abstract fields such as algebra. Seeing mathematics as pictures or diagrams, not just symbols, may help students better understand the concept and see the creativity in mathematics. While teaching the sum of a converging infinite geometric series, I usually present students geometrical interpretation of some examples. Let's imagine the geometric series 1/4 + 1/16 + 1/64 + ... as areas of purple squares. The sum of the areas of the purple squares is one third of the area of unit square, so it is equal to one third. The same result we can obtain using pattern for sum of a converging geometric series.

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Ewa -Effective teamwork and collaboration and mathematics.

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Ewa -Effective teamwork and collaboration and mathematics.

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The benefits of collaborative learning are multiple. Firstly, students develop thinking skills and communication skills. Moreover, they have to challenge in understanding of diverse perspectives, and to do it they have to be good listeners. To enhance students teamwork I make sure, that they work in small groups on a complex task, that requires participation of all members. At the end of the exercise, students get a chance to evaluate their own participation and effort.

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While choosing interesting math applications in local context, to be considered in classroom, we should focus on local situation. Which issue will be important for community in next years? With what ecological problems they are struggling? And so on. We should first show students real-life examples of application of mathematical knowledge, and by that encourage students to apply math in contexts outside the math classroom. For example, we can talk about interests in context of loans or investments in local banks.

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Billy - Teaching differentiated to meet the needs of all learners

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Billy - Teaching differentiated to meet the needs of all learners

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With the recent year forcing many of us to go online, I began to find new ways to differentiate instructions, while also creating a universal design so everyone has access to all these resources. For example, I have began recording the lessons while I am teaching. This allows students who would rather be consistently engaged in the lessons and not able to write everything down to focus on the concepts and then rewatch the lessons later to create notes for themselves. Another thing that I have done is adjusting assessments based upon the needs of the students. Some students are unable to process information through a written component on a small sheet of paper, so providing students with the chances to do an oral presentation or take over a white board to demonstrate their understanding on a larger canvas.

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Billy Teaching focused on effective teamwork and collaboration

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Billy Teaching focused on effective teamwork and collaboration

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While working in my classrooms, I have been putting a larger emphasis on a thinking based classroom. Students are separated into groups of 3-4 and asked to solve a series of problems based on a new topic. The lesson begins with a problem that makes connections to a previously learned concepts that will help them throughout the lesson. The questions then begin to move up in difficulty and students try new strategies and come up with ways to solve new problems. As the students work through the lessons they are continually bouncing ideas off each other and trying to determine a variety of techniques that could work to solve a problem

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While in my classroom, I like to provide students with multiple opportunities for formative style assessments. They can start off by being quizzes so they have an idea of what some assessments might look like. As time moves on, they begin to move to formal conversations so that their communication skills can improve as well. This not only helps the students can a better understanding of the topics and where they stand, but allows me to determine if I need to go back and revisit a concept