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For DI and P&D

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Example only

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Example only

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When the strategies in this element produce the desired effects, teachers will observe the following behaviours in students.
Students actively identify and analyse their own errors.
Students actively identify and analyse others' errors.
Students can describe and exemplify the different types of errors one might make.
Students can explain how the activities have increased their understanding of the content.

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When the strategies in this element produce the desired effects, teachers will observe the following behaviours in students.
Students understand the similarities and differences between the elements being compared.
Students ask questions about the similarities and differences between the elements being compared.
Students can explain how the activities deepened their knowledge.

Element 11: Examining Errors in Reasoning

This element helps deepen students' understanding of content by having them examine their own reasoning or the overall logic of information presented to them. Such activities are at the core of what is referred to as "college and career readiness" (Conley, 2014). This makes intuitive sense in that students who are ready for college and careers have the ability to analyse their own or others' thinking.
This element aligns to the Dakabin State High School vision, ensuring that students are equipped with the skills necessary for work or careers in the 21st Century.

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When the strategies in this element produce the desired effects, teachers will observe the following behaviours in students.
Students actively engage in practice activities.
Students ask questions  about the procedure.
Students increase their competence with the procedure.
Students increase their confidence in their ability to execute the procedure.
Students increase their fluency in executing the procedure.

Element 10: Examining Similarities and Differences

The element helps students deepen their understanding of declarative knowledge by examining how things are alike and not alike. Strategies within this element apply to both declarative and procedural knowledge.

There are fourteen strategies within this element; therefore, a teacher could engage students in a great deal of knowledge-deepening activities involving similarities and differences without repeating any given strategy. Some of the strategies involve the use of specific graphic organisers, while some involve the use of abstract characteristics like similes and metaphors. Some strategies, like classification charts, involve variations on how one might define similarities and differences.

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Once content is introduced through direct instruction, teachers must further develop student knowledge.

When conducting practicing and deepening lessons, it is important to mind the difference between procedural and declarative knowledge.
Procedural knowledge includes skills, strategies and processes.
For example: converting fractions to decimals, decoding, and writing an expository essay, as it involves executing multiple strategies that have different outcomes but must work together in a unified manner.

Declarative knowledge involves information. It too comes in a variety of forms.
At the lowest level, it involves knowledge of terminology. The next level includes facts. Both terminology and facts are relatively specific and together are referred to as details.
At a much broader level are generalisations and principles. They organise terms and facts into related sets of information.
Example: Generalisations describe the angles of a triangle including the sum of the interior angles and angle-angle similarity and congruence.
Principles describe the relationship between variables; for example, as one variable increases, the other decreases.
At the highest level of organisation are concepts.
Concepts organise generalisation and principles into bigger systems of information. For example, the concept of a polygon can organise generalisations, principles, and details about triangles, rectangles, trapezoids and the like.

The following elements are important to effective practice and deepening lessons.

Element 9: Using Structured Practice Sessions.

Practice is a staple of effective teaching, but it is commonly misunderstood.
One obvious consideration is that practice applies to procedural knowledge, not declarative. That is, students need to practice skills, strategies and processes. They do not need to practice details, generalisations, principles, and concepts. Rather, students deepen declarative knowledge through other types of activities (Element 10 and Element 11).

Procedural knowledge progresses through three stages:
1. Cognitive
2. Associative
3. Autonomous

1. At the cognitive stage, students are simply learning about the skill, strategy or process. They are learning declarative knowledge. Students are not executing anything at this stage, rather they are trying to understand what you do first, what you do next, and so on.

2. At the associative stage, students are trying out the strategy and determining which parts they have to alter to augment to make the strategy efficient and effective for them personally. This is the phase that requires the most analysis by students since they have to determine which parts of the procedure they might change.

3. At the autonomous stage, students are fine tuning their ability to execute the procedure and developing fluency in its use.