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Wiggins and McTighe (2006a)

1) Activity-oriented design in which activities do not lead to any intellectual challenge or development. "Hands-on without being minds-on," they're time-filling activities that don't focus on authentic conceptual understanding.

2) content coverage with little understanding of the concepts by the learner. Coverage right now is equated to learning and understanding when the problem of this belief was recognized more than 2000 years ago.

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These types of questions are used to evaluate the conceptual understanding of a topic. They're most helpful to bridge different areas of mathematics with a "what do we know" to a "what do we wonder" type of structuring. They are best used at the beginning of a unit to seek prior knowledge, during a unit as a form of formative assessment to focus the instruction on what needs improving, and at the end of a lesson as a summative tool to assess the achievement of the topic.

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Using visible thinking, students are able to express and communicate their personal thoughts and ideas. This helps teachers to gain insight into students' thinking about the topics of interest.

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When students are given the opportunity to reflect on what they have learned in a topic, specifically what they should and shouldn't do, written visibly next to each other, they can be helpful for identifying classic mistakes students make. As well as a way for teachers to see and remind them of topics they gathered throughout a lesson or unit.

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The use of these skills can lend to creating core skills such as communication, self-management, and research skills. By structuring a class curriculum that actively uses visible thinking routines, students get into the habit of thinking conceptually about their math and how to find important findings throughout their learning experience. Students also learn helpful ways to document findings and carry on with them in the future.

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Students develop the skill of communication by staying true to what they understand about the topics. Going through exercises where one's opinion can easily differ from others and then having them explain their beliefs is a great way to foster open communication and allow for differences of opinions in a constructive and supported way. This leads to more confidence in communicating one's thoughts.

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Mastery of self-management can be seen when students independently seek to extend the assigned work, express enthusiasm and genuine interest in the challenge of the work, demonstrate self-discipline and persistence with longer-term and more complex work, value and seek collaboration to complete the tasks and show an equal interest in the learning process as producing a quality product.

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Students can develop their research skills by completing "RAFTS" (role, audience, format, topic) and "GRASPS" (goal, role, audience, situation, performance, standards). These performance tasks promote the development of quality performance tasks and complement finding the importance of what you are trying to attain in research.

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Self-assessment strategies can develop metacognitive abilities, which involve students being able to self-monitor and reflect. Research supports that developing students’ ability to become more self-aware of and engaged in their own learning helps student achievement. Students can be encouraged to reflect through self-assessments. Self-assessments are best used once at the beginning and once at the end of a unit to track starting and finishing points. They are also a great way to show progress/achievement without grades.

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Visible thinking routines (from Harvard University’s Project Zero) are strategies to make student thinking visible. These routines allow learners to express and communicate thoughts and ideas.

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A widely used assessment tool, which provides opportunities for learners to identify different attributes of a concept by looking at examples as well as non-examples to show conceptual understanding. It can help students build mathematical vocabulary skills as well as enhance their knowledge of math concepts. It is best used when introducing completely new topics and vocabulary, such as trigonometry when introducing sine cosine and tangent, right triangles, etc.