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Main guiding purpose should eb to inform teaching and learning and "sit beside" the student by guiding them to new knowledge. We do not have to just "teach to the exam"

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Help identify student pre-existing knowledge which in turn helps inform instruction. One common example is "Write everything you know about.....". This is a valuable strategy as it steers students away from what they don't know about something to what they do know.

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When: At the end of the unit after student build their foundational knowledge, you can use them to help explore and connect ideas. Can also be used at the beginning of unit as a diagnostic tool to seek prior knowledge or content.

Why: Want to see the kind of conceptual connections students form between different areas of mathematics.

How: Provide open ended questions where there could be multiple ways in whcih students can take them. Also want them to come up with their own conceptual examples. For example, "When is the cosine rule used? (Give an example) and Explain sinx, cosx, and tanx.

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When: Can be included at end of the year or as a project to break up the semester.

Why: Want students to be able to communicate mathematical ideas in a coherent fashion. This way they can have opportunities to pursue areas of math not covered by standard exams and to cultivate an overall appreciation for mathematics. Areas include sports, gambling, transport, etc

How: Give students their choose in their line of inquiry and topic. Criterion focused type of assessment with criteria being (Communication, Math presentation, personal engagement, reflect and use of math)

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Want student to be able to transfer and apply knowledge to new, unfamiliar scenarios.

Allow for differentiation of abilities (Ex: One value for theta is _, Name five other possible values if...)

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1) Allows students to express and communicate their personal ideas

2) Gives teachers diagnostic and formative feedback while giving insight into students thinking

3) Allows for students to possibly collaborate with each other and connect to each others learning

4) Are an important tool for cognitive closure which can give opportunities for students to come up with questions and clarify and misunderstandings

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I can apply visible thinking routines throughout the entirety of a unit or lesson

1) Headlines - can use at the end of the unit where students write down a headline that summarizes key ides and concepts form a lesson (great Check For Understanding)

2) I use to think.... Now I Think.... can be a great formative assessment or part of an exit ticket to help students explain what they have learned in a specific day

3) Generate, Sort, Connect, Elaborate - my current mentor teacher uses this strategy in which students generate as many ideas about a concept as possible. Then they sort them by concepts, connect them to each other, and elaborate on their importance and why they connect (Good for showing and expanding on overall math connections)

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Are considered "complex challenges that mirror the issues and problems faced by adults" (Wiggins, Mctighe 2006). They help asses what student understand, what they know (Factual knowledge), and what the can do (skills)

When designing performance tasks want to follow the what, why, how model or use the acronym RAFTS which means, Role, Audience, Format, Topic, and Strong verbs/adjectives.

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Want something that is real world applicable and can have base diagrams off of.

INFORMATIONIS MOST LIEKLY TO GET STORED IF IT MAKES SENSE AND HAS MEANING

In this case something like ratios and proportions, trigonometry or geometry concepts such as perimeter/area, functions and algebraic thinking, etc.

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I have seen and used a variety of graphic organizers to help students show their knowledge. Some that are mentioned in the text include...

Agree, Disagree, Depends - there is a sign on each the walls of the room that says these things, then a statement is given and students walk to what they agree with (GREAT KINISTHETIC ACTIVITY)

Frayer Model - my mentor teacher has Frayer models for each major concept that she gives as homework, students have to think about examples and non examples which is an important skill

Problem Solving Maps - one example I have used in my schooling and can be used with students is a map in which students are presented a longer, more difficult problem and are asked these questions, 1)What do I know? 2) What do I need to find 3) What strategy will I use?

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Developing Essential Skills in a Math Classroom

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Developing Essential Skills in a Math Classroom

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Five main categories of skills are communication, social, self management, research and thinking. These can be developed through emphasizing conceptual understanding and developing multiple contexts for each unit.

Actions in Classroom: In order to achieve these skills we want to use more inquiry based lessons, focus on giving students more time to collaborate, and change up the forms of assessment to allow for differentiation and multiple ways for students to express understanding.