EDCU 13020 Mathematics curriculum

Assessment Task 1 – Downloadable instructions

Task Description

Topic: Creating a Diagnostic Assessment Activity

Weighting :    50%

Task: Individual written submission

Word count: 2000 words

Due date: Thursday August 26, 2021 11:45pm AETD

Introduction:

Teachers are required to know the Australian Curriculum: Mathematics content; how to teach it and how to assess it.  This professional knowledge enables teachers to construct assessment activities to plan for, and implement, quality teaching and learning practices that support students’ engagement and learning in mathematics.  Assessment is ongoing throughout the teaching and learning process, not a  point of time procedure at the end of a topic.

Rationale :

This assessment task aims to develop your understanding of the Australian Curriculum: Mathematics, to build your professional knowledge and skills for assessing students’ mathematical understanding, and to assist you in planning and teaching mathematics effectively. The knowledge and skills developed from this assessment will support your ability to notice students’ mathematical thinking. In addition, you will be able to develop the skills that promote students’ structural thinking, conceptual understanding, engagement and motivation. By focusing on assessment as, for and of learning you will support learning sequences that are found in the Australian Curriculum: Mathematics Proficiency Strands of fluency, problem-solving, understanding and reasoning.  

Additionally, the Australian curriculum states : “Teachers are expected to teach and assess general capabilities to the extent that they are incorporated within learning area content.” (ACARA, 2021). General Capabilities foster a deep understanding of the structure and the progression of concepts through the development of critical and creative thinking skills, and personal and social capability that promote self awareness and management as well as social awareness and management. These capabilities can be associated to the proficiency strands to  assist in dveloping deeper structural awareness and conceptual understanding of mathematics.  

This knowledge and these processes will support your capacity to create appropriate and effective assessment strategies.

Task Description :

This task requires you to examine the relationship between curriculum, pedagogy and assessment and apply your knowledge and understanding to develop and enhance your teaching and assessment practices in mathematics.

In this task, you are to create a diagnostic assessment activity that is embedded in a mathematics lesson. The lesson will focus on one content descriptor from the Number and Algebra strand of the Australian Curriculum: Mathematics and will demonstrate how you address assessment is used as learning, for learning and of learning.  You will need to include the mathematical proficiency strands and the general capabilities in your lesson as how you will teach and how you students will learn.

To complete the task you will need to:

Step 1

Select one content description from the Year 1 or 2 Number and Algebra content strand that will be the focus context of your task along with the Proficiency Strands and the General Capabilities from the Australian Curriculum (ACARA, 2021)

Step 2

Examine the progression and development of the content knowledge in relation to your chosen content description. Consider also how the proficiency strands and general capabilities will support your development of a diagnostic assessment activity to identify students’ learning.

You should also refer to the relevant knowledge element in the Number Sense and Algebra section of the National Numeracy Learning Progression to ensure that the numeracy capability associated with the content descriptor is included in the analysis. 

Refer to the relevant knowledge element within National Numeracy Learning Progression to prompt your understanding of the conceptual understanding associated with the content description.  Consider learners with differing levels of prior knowledge from diverse backgrounds, including individuals from various linguistic, cultural, religious, educational and socioeconomic backgrounds, and students who identify as Aboriginal and/or Torres Strait Islander. 

Step 3

Describe the issues for teaching, learning and assessing student understanding this mathematical content.

Propose and discuss pedagogical responses to the barriers you have described, and consider how the proficiency strands (Understanding, Fluency, Problem-solving, Reasoning) may be reflected in the teaching and learning responses. You should engage in personal research to identify specific teaching responses that enable learners from diverse backgrounds to engage with the mathematical thinking.  Be sure to justify your discussion withprofessional literature.

You need to consider how to embed your diagnostic assessment activity so it identifies assessment as, for and of learning. What does this mean and how do you implement these processes in a classroom?

Analyse potential barriers to learning the proposed content  description in terms of factors that may impact on the learners’ experience of the conceptual understanding. 

Give evidence from research of the misconceptions related to your content description. This research process is important for developing an understanding of the types of misconceptions and knowledge gaps specific to the mathematical concept chosen, which are revealed when monitoring students’ conversations or written work. It will also help you understand how students’ think mathematically and how their mathematical thinking influences how they learn and understand mathematical concepts.   

This could involve other areas of mathematical research that relates to your chosen concept, such as: problem solving, mathematical thinking, conceptual and procedural understanding, structural or relational thinking, students’ anxiety in learning mathematics, students engagement in mathematics and socio-constructivist learning in mathematics.

The knowledge you gain through conducting this research will be used to frame your diagnostic assessment activity.  Therefore, it is important that your research be specific to the mathematical concept that you have analysed. This research requires you to explore the current research literature in this area. The research in this area is significant and large, you may need to limit your research.

Step 4

Create a diagnostic assessment activity that is embedded in your mathematics lesson, that can be identified as:

  • the students’ learning (assessment as learning);
  • appropriately determines the students’ current knowledge (assessment of learning); and,
  • gives you as the teacher direction for future learning (assessment for learning).

You should also consider the students’ prior learning (National Numeracy Learning Progression) and readiness to learn the content for a planned sequence of learning that will focus on the selected content description. 

For your chosen  Number and Algebra Strand content description you will create a knowledge analysis  profile to help you align your Year 1 or 2 diagnostic assessment procedure, you  should create opportunities to address conceptual knowledge for this content from your knowledge analysis. 

This diagnostic assessment activity should then reflect your research and facilitate opportunities, for you as the teacher to to identify the level of understanding achieved by students. Students’ understanding also includes what they do not understand due to misconceptions or inefficiencies that have hampered their ability to learn the content;  refer to to research for evidence of why students may not engage in the learning of the content. 

Your diagnostic assessment procedure should be a response to what you have learnt about how students think mathematically to develop their structural awareness of mathematics that results in a conceptual understanding of mathematics. This development should support students engagement and motivation in learning mathematics.  

 Step 5

Develop an assessment marking guide to accompany the assessment activity you have created. This should include aspects of your research, such as: misconceptions, engagement, structural awareness, conceptual understanding, and justify their inclusions as part of your assessment. You should reflect the Australian Curriculum: Mathematics Year 1 or 2 Achievement Standards.  You can use the Australian Curriculum: Mathematics work samples as a guide. You need to consider explanations that identify the potential misconceptions or inconsistent understanding, which may contribute to the error, to address why a student might not accurately apply mathematical thinking.  

Step 6

Reflect on how this assessment task provided a context for your professional learning, and why opportunities for professional learning are significant in terms of professional practice.  This component is a personal reflection and therefore, this section of the assessment should be written in first person.  You should make specific links between the processes you engaged in for addressing the task requirements, your professional learning and the potential to improve student outcomes.  Be sure to use examples from your assessment process to evidence your professional learning as you prepare to teach the Australian Curriculum: Mathematics.

 

Possible Format :

Cover page

Contents page

Written response (included in your word count)

Sections Headings:

  1. Introduction and background (300 words)
  2. Literature Review (Research evidence) (500 words)
  3. Conceptual Framework (How your research frames your assessment strategy) (500 words)
  4. Discussion (How you used assessment as, for and of learning) (500 words
  5. Conclusion (How this task added to your professional learning) (200 words)

Please note: word count above is given as a guide only

Extra information (not included in your word count)

References (APA 7 style)

Appendix 1 – Knowledge Analysis graphic organiser

Appendix 2 – Diagnostic Assessment Activity (you can include your pedagogical strategy)

Assessment Criteria : 

Knowledge and understanding of the concepts, substance and structure of the content in the Mathematics curriculum (APST 2.1) 

Ability to create and modify appropriate assessment tools that determine students’ prior knowledge and achievement and understanding of mathematical concepts (APST 5.1)

Knowledge and understanding of barriers to mathematical proficiency and appropriate pedagogical responses to differentiate for diverse learning needs (APST 1.1, 1.2, 1.3, 1.4, 2.5)

Demonstrated understanding of the relationship between professional learning for teachers and improved student outcomes (APST 6.2, 6.4)

Application of academic writing conventions and adherence to APA style and referencing

Assessment Criteria Grid

 High Distinction    50 – 42.5Distinction         42.49 – 37.5Credit              37.49 – 32.5Pass                   32.49 – 25Fail                            24.9 – 0
  Knowledge and understanding of the concepts, substance and structure of the content in the Mathematics curriculum    Excellent examination of the progression and development of the content knowledge in relation to your chosen content description. Excellent consideration of how the proficiency strands and general capabilities support the development of students’ learning. Excellent exploration of the numeracy learning progression, and consideration of the curriculum content and structure.  Very good examination of the progression and development of the content knowledge in relation to your chosen content description. Very good consideration of how the proficiency strands and general capabilities support the development of students’ learning. Very good exploration of the numeracy learning progression, and consideration of the curriculum content and structure.  Good examination of the progression and development of the content knowledge in relation to your chosen content description. Good consideration of how the proficiency strands and general capabilities support the development of students’ learning. Good exploration of the numeracy learning progression, and consideration of the curriculum content and structure.  Satisfactory examination of the progression and development of the content knowledge in relation to your chosen content description. Satisfactory consideration of how the proficiency strands and general capabilities support the development of students’ learning. Satisfactory exploration of the numeracy learning progression, and consideration of the curriculum content and structure.  Unsatisfactory examination of the progression and development of the content knowledge in relation to your chosen content description. Unsatisfactory consideration of how the proficiency strands and general capabilities support the development of students’ learning. Unsatisfactory exploration of the numeracy learning progression, and consideration of the curriculum content and structure.
  Ability to create and modify appropriate assessment tools that determine students’ prior knowledge and achievement and understanding of mathematical concepts  The creation of a valid, quality diagnostic assessment incorporates productive methods of mathematical understanding to facilitate accurate measurement of students’ prior knowledge, across a range of ability levels. A comprehensive understanding of the progression of knowledge associated with the content descriptor is evidenced and sophisticated opportunities to effectively evidence understanding, fluency, reasoning and problem solving, in relation to the focus concept, are apparent.  The creation of a valid diagnostic assessment incorporates effective methods of mathematical understanding to facilitate measurement of students’ prior knowledge, across a range of ability levels. A well-developed understanding of the progression of knowledge associated with the content descriptor is evidenced and well-considered and relevant opportunities to evidence understanding, fluency, reasoning and problem solving, in relation to the focus concept, are apparent.  The creation of a diagnostic assessment draws on appropriate methods of mathematical understanding to facilitate measurement of students’ prior knowledge, across a range of ability levels. A sound understanding of the progression of knowledge associated with the content descriptor is evidenced and intentional opportunities to evidence understanding, fluency, reasoning and problem solving, in relation to the focus concept, are apparent.  The compilation of a diagnostic assessment incorporates a basic interpretation of the methods of mathematical understanding to facilitate measurement of students’ prior knowledge. A basic understanding of the progression of knowledge associated with the content descriptor is evidenced and some consideration of opportunities to evidence understanding, fluency, reasoning and problem solving, in relation to the focus concept, is apparent.  The diagnostic assessment evidences limited consideration of the methods of applying mathematical understanding. Opportunities to measure students’ prior knowledge indicate limited, superficial or inaccurate understanding of the progression of knowledge associated with the content description and consideration of opportunities that evidence understanding, fluency, reasoning and problem solving, in relation to the focus concept, is narrow or lacking intention.
   Diagnostic assessment marking guide provides authentic anticipated student responses, including errors, and effectively directs future teaching of the concept. Incorrect answers are accompanied by clear and informative explanations that identify the misconceptions revealed in the errors.  Diagnostic assessment marking guide provides highly appropriate anticipated student responses, including errors, and directs future teaching of the concept. Incorrect answers are accompanied by clear explanations that identify the misconceptions revealed in the errors.  Diagnostic assessment marking guide provides appropriate anticipated student responses, including errors, and supports future teaching of the concept.  Incorrect answers are accompanied by explanations that identify the misconceptions revealed in the errors.  Diagnostic assessment marking guide provides anticipated student responses including errors. Incorrect answers are accompanied by basic explanations that identify errors and gaps in mathematical thinking.  Diagnostic assessment marking guide exhibits limited or insufficient understanding of the pedagogical purpose of a diagnostic marking guide in directing future teaching through identifying issues with mathematical thinking, revealed in errors or misconceptions.
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