Developing+Declarative+&+Procedural+Knowledge


 * Developing Mathematical Knowledge**  **and Ways of Working!**


 * While the Australian Curriculum and Mathematical guidelines provide an excellent resource for depicting the expectations and knowledge content for students at each year level it doesn't necessarily explain how students acquire declarative and procedural knowledge. See the graphic organisers below for examples of how this knowledge is developed and assessed. Also see __beneath__ each graphic organiser for classroom activities which can support this development (ACARA, 2012).**

=**Purpose**=
 * Table 1: Modelling and problem-solving task: **

This technique is used to assess students’ abilities to respond to a specific task or issue that highlights a real-life application of Mathematics.

=**Description**=

• A modelling and problem-solving task may require a response that involves mathematical language, appropriate calculations, tables of data, graphs and diagrams.

• When completing the modelling and problem-solving task students may:

− analyse information and data

− process information

− interpret and synthesise data

− explain relationships to develop and support mathematical arguments

− reflect on and evaluate data, propositions, results and conclusions

− communicate ideas.

=**Format**=

The presentation format of a modelling and problem-solving task will typically be written and should be supported by the appropriate use of data, calculations, diagrams, flowcharts, tables and graphics. Examples of modelling and problem-solving task presentation formats include:

• oral, electronic or multimodal presentations

• computer-generated simulations

• virtual models using computer software

• construction of 2-D or 3-D models.

=**Conditions**=

A modelling and problem-solving task can be:

• undertaken individually and/or in groups

• prepared in class time and/or in students’ own time.

=**Purpose**=
 * Table 2: Mathematical Investigation: **

This technique is used to assess the abilities of students to respond to an authentic challenge or a researchable context or situation.

=**Description**=

• A mathematical investigation should be conducted over an extended time frame. Challenges, contexts or situations could include:

− mathematical experiments

− field activities

− case studies

− feasibility studies

− proposals to a company or organisation.

• A mathematical investigation in a P–2 context is guided. It involves students and teachers collaborating to gather and record information.

=**Format**=

The presentation format of a mathematical investigation will typically be written and should be supported by the appropriate use of data, calculations, diagrams, flowcharts, tables and graphics. Examples of mathematical investigation presentation formats include:

• reports

• brochures

• journals

• graphic organisers

• oral, electronic or multimodal presentations

• computer-generated simulations

• virtual models using computer software

• construction of 2-D or 3-D models

• blogs and wikis

• podcasts and short videos

• peer and self-reflections.

=**Conditions**=

A mathematical investigation can be:

• undertaken individually and/or in groups

• prepared in class time and/or in students’ own time.

=**Purpose**= This technique is used to assess student responses that are produced independently, under supervision and in a set time frame. A supervised assessment ensures there is no question about student authorship.
 * Table 3: Supervised Assessment: **

=**Description**=

• Supervised assessment items will be in response to questions or statements. Questions or statements are typically unseen. If seen, teachers must ensure the purpose of this technique is not compromised.

• Stimulus materials may also be used. Stimulus materials may be seen or unseen.

• Unseen questions, statements or stimulus materials should not be copied from information or texts that students have previously been exposed to or have directly used in class.

=**Format**=

Examples of supervised assessment presentation formats include:

• questions

− Items may also include multiple-choice, single-word, true/false or sentence answers. These types of questions are useful for assessing content knowledge and are difficult to construct if trying to elicit meaningful high-order cognitive responses.

• prose

− Items may include responses to stimulus activities that require

 explanations longer than one sentence

 responses to seen or unseen stimulus materials

• practical exercises and calculations

− Items may require students to

 construct, use, interpret or analyse primary or secondary data, graphs, tables or diagrams

 apply algorithms or demonstrate mathematical calculations and problem solving.

=**Conditions**=

Supervised assessment items will typically:

• be undertaken individually

• be held under test/exam conditions

• allow perusal time, if required

• use stimulus materials that are succinct enough to allow students to engage with them in the time provided. (If stimulus materials are lengthy, they may need to be given to students prior to the administration of the supervised assessment)

• be completed in one uninterrupted supervised session or a number of supervised sessions.

=**Purpose**= This technique is used to record evidence of children’s ability to use mathematical skills and communicate mathematical understanding in a task or within mathematical activities.
 * Table 4: Observation Records: **

This technique is predominately an early years assessment technique, though it is not confined to the early years.

=**Description**=

An observation record is collection of evidence gathered by teachers about children’s learning. It can include:

• anecdotes and observations that show children measuring and comparing during everyday activities within a range of contexts

• work samples that

− demonstrate children directly comparing pairs of objects using uniform informal units

− show children reasoning and working through drawings, diagrams and written responses to measurement activities

• questioning and interviewing small groups of children to enable them to explain their reasoning and demonstrate what they know and can do, conducted within a planned assessment task or within mathematical activities

• a checklist that records written teacher comments on the selected skills and understanding demonstrated by the students.

An observation record can provide opportunities to record assessment evidence reflecting the proficiency strands:

• Understanding

• Fluency

• Problem solving

• Reasoning

=**Format**=

The format of an observation record is developed by teachers.


 * References:**

Queensland Studies Authority. (n.d.). //Advice on Implementing the Australian Curriculum P- 10.// Retrieved from: []