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Teaching informed by assessment (formative and summative)

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Teaching informed by assessment (formative and summative)

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I think teaching informed by formative and summative assessment is very important. As the assessment is formative, so the students must seriously learn every lesson. As the assessment is summative, so students should recover all the knowledge they have learnt timely.

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Traditional teaching emphasize engrafting ready knowledge to students.  This kind of teaching has an obvious disadvantage, that is students could not solidly grasp the knowledge and they will forget the knowledge they learned very quickly. While teaching based on inquiry can deepen students' understanding about the  knowledge, for example, they will know the generated background of the knowledge, the theoretical and real-world application of the knowledge, etc.

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Teaching differentiated to meet the needs of all learners

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Teaching differentiated to meet the needs of all learners

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In a class that has about 20 students, if we teach all the knowledge at the same level, then some students may master the knowledge very well while others may  couldn't master it. Therefore we should differentially teach to cater different needs of students, for example, as to some brilliant students we may teach them some advanced and difficult knowledge , while for some people, we may take more time to help them master the basic knowledge.

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“The Great aim of education is not knowledge but action” - Robert Spencer

During this pandemic when more and more teachers and facilitators have turned to technology for teaching purposes, this approach can be highly effective to teach students in a mathematical Classroom. The teachers can share their screen along with the students and use the feature of ‘Google Earth’ and show the students detailed structures of different architectural marvels which uses basic mathematical concepts like Geometry and trigonometry to create beautiful structures s such as ‘The Gherkin’ in London which is a parametrically designed solid of revolution and Kandariya Mahadeva Temple in Khajuraho, India, which is an example of immaculate architecture with a fractal-like structure which has many parts that resemble the whole.

This activity showcases the immense possibility of application of mathematical concepts like Geometry & Trigonometry which can in turn inspire the students to study these concepts more enthusiastically in the classroom.
https://earth.google.com/web/search/The+Gherkin,+Saint+Mary+Axe,+London,+UK/@51.51451128,-0.08027774,191.85180131a,44.97282296d,35y,145.37554029h,2.52250633t,0r/data=CigiJgokCeIwL2W0TlRAERSU_w8UgB3AGbXMp36Ue1pAIRSlnTDisGDA

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In this approach the teacher uses the ‘Connect – Extend – Challenge’ Approach. The teacher first explains the basics of the topic by connecting it to a real-life situation. After which a solution to that problem is provided in the form of a theorem or formula. After which the students are provided with a set of problems when they solve by themselves either at home or in class. This makes the students go over the concept a few times and that in turn inculcates better comprehension of the topic.

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In this approach, a separate topic or portion of a Module is assigned to each of the students and they are then required to go home and prepare the topic through their textbooks and through videos online which shall also be provided to them by their facilitators. Then they have to present the Topic in front of the rest of the class. I believe that through this approach :1) The student takes an active intent towards understanding the concept so as to present it in front of the class and 2) Allows the facilitators to get a glimpse into the areas in which the each student might need help to understand and fill in their blanks, if needed.

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Investigations:  Technology use because it is quick and broad

Open-ended problems:   Unit problems introduced at the beginning of the unit.  Students can read and visit the problem throughout the unit to think about it.  Small prompts:  In what ways might we use the concept or content to approach our unit problem? These could help lead to conjectures when we begin to work on the problem.

Use cycle of inquiry when designing inquiry-based problems.

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Standards based grading would be good so students and teacher can get feedback on which objectives are known and which need reteaching, and could help prepare for the diploma assessments.

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Geometry has many opportunities for discovery learning. Formulas such as distance or Pythagorean Theorem can be discovered.
For triangle congruence, give students three pieces of a triangle and see if they can make different triangles or if everyone makes the same triangle and what does that mean.

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Present material in different ways: sometimes direct instruction or sometimes through a flipped classroom where students can watch videos at home and then work on problems in class.

Have challenge problems at the end of homework or on tests for enrichment for students who need it.

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Set up teams early in the year.  Have them name themselves.  Allow them some choice (sometimes students just do not get along).  Teach them how to collaborate by having students establish the rules as a class and agree on those rules.  If necessary (one student always leads for example and one is always very quiet)  rotate roles of the group.  Observe group interactions for what works and what doesn’t.  Students reflect

Pair work:  Vary the type of groups they work in.

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Align lessons and units with concepts and the content-specific conceptual understandings for each topic in the planning stage.

Desmos can be done individually or in groups and has some lovely conceptually based introductions and explorations of mathematical topics.

Strategies:  assess pre-instructional understandings, four square, examples and non-examples, chalk talks (can be done on padlet), uncover (through inquiry), and transfer (through extension)