MATHEMATICAL CONTENT KNOWLEDGE -
The topic that is being assessed is on geometry, more specifically two-dimensional and 3-dimensional
shapes and their properties. Properties that are being assessed will include faces, vertices, and edges.
In teaching 2D shapes, it is important for students to develop knowledge on recognising shapes
(knowing which are examples and non-examples), and using everyday objects and determining which
shape they are. They should know the common names and use common vocabulary. Teachers should
provide students with opportunities to explore the properties or solve problems. Common 2D shapes
include triangles, quadrilaterals, pentagon, hexagon, octagon, decagon and dodecagon.
Student misconceptions:
Students commonly mistake vertices for edges or vice versa, as well as thinking that the face on the
bottom of a 3D shape is not included because it is unseen. Students often confuse hexagons,
pentagons or octagons with each other, or believe that they all have sides the same length.
PEDAGOGICAL CONTENT KNOWLEDGE -
Different types of grading for mathematics include:
- Performance based assessment - connected to actual problem-solving activities used in instruction.These include concepts such as shares, decimals, or mental math.
- Rubrics - a rubric is a framework that can be designed or adapted by the teacher for a particular group of students or task. It consists of a scale of 3 to 6 points that is used as a rating of performance on a single task rather than a count of how many items in a series of exercises are correct/incorrect.
- Simple rubrics - E.g. the New Standards Project developed a simple four-point rubric of 1 (unsatisfactory), 2 (marginal), 3 (proficient), and 4 (excellent).
- Performance indicators - task specific statements that describe what performance looks like at each level of the rubric.
Observation tools in assessment include:
- Anecdotal notes - writing short notes during or immediately after a lesson in narrative style.
- Observation rubric - 3 or 4 point generic rubric on a form to jot down names of students and space for quick comments.
- Checklists for individual students - using sticky notes or cards
- Checklists for full classes - listing all students on a single page in grid form
Assessments include:
- Writing and journals - assess their quality of writing as it requires gathering, organizing, and clarifying thoughts
- Student self-assessment - Getting students to answer questions (how well do you think you did? What is one thing you liked? What was your contribution in this group activity?)
- Diagnostic interviews
- Tests
Formative Assessment: Given throughout the learning process, formative assessments
seek to determine how students are progressing through a certain learning goal.
Summative: Given at the end of the year or unit, summative assessments assess a student's mastery of a topic after instruction.
Reference: (Van et al., 2015)
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Activity - Assessment on Geometry (Shapes)
Year Level - 1
Classroom Context -
Teachers must be aware of socioeconomic diversity in the classroom as this can great impact student
well-being and academic performance. Although this is an area that can be difficult for educators to
detect in the class, there are various ways to plan active and inclusive teaching methods to engage
students of low socioeconomic status (SES). These include face-to-face time with the teacher and
creating a classroom environment of accessibility.
Content Descriptor -
Recognise and classify familiar two-dimensional shapes and three-dimensional objects using obvious
Resources -
Recording sheet for the teacher, assessment question sheets for the students, grading criteria/system
Prior Knowledge -
Uses everyday language to describe and compare shapes and objects
Finds similar shapes or objects in the environment
Identifies and describes features of shapes and objects
Describes what an object may look like from a different perspective
Assessment Item -
For this assessment activity, grade 1 students are assessed on their ability to recognise and classify
two-dimensional and three-dimensional shapes. Geometry is introduced in the early years of schooling,
such as Foundation years. It is an important concept to learn, as a strong understanding of shapes is
vital for learning more complex geometry concepts later on. Examples include modelling, constructions
and whole-brain thinking (Kotze, 2007).
- This assessment will take place at the end of the unit, to determine what level the students are at.
- They have been learning this concept during classroom activities and it has been continuously looked at over the unit.
- During periods such as quiet individual reading times, or when students are busy working with other activities, call out students one by one to perform a task-based interview.
- During the interview, use a recording sheet to record their responses and answers. Note down any comments.
- Provide the student with a collection of shape examples on a worksheet.
- Ask them each question one by one, to identify their understandings, errors, strategies and reasonings.
- Use a simple four-point rubric by the ‘New Standards Project’ to determine their score.
- Provide immediate, constructive and instructive feedback to the student.
- Identify which areas the student can improve on, and reflect/modify your lesson unit.
- Students who achieve one to five questions right will achieve score 1 (Unsatisfactory), those who achieve six to nine will receive a score of 2 (Marginal), those who achieve ten to fourteen will receive a score of 3 (Proficient), and student those who achieve fifteen to full marks will achieve a score of 4 (Excellent).
Images -
Scoring criteria used
Assessment sheet for students to refer to
Reflection -
This week, we looked at the different types of assessment in mathematics. An article by
Callingham (2010) discusses that assessment is the most powerful element in teaching and
learning. For it to be helpful, it must be broad ranging, collecting a variety of information using a
range of tasks before, during and after a teaching sequence. There are both strengths and
weaknesses in each form of assessment, for example, summative assessment have many
advantages because they provide motivation to students to study and pay attention in class.
However, summative assessments are often not enjoyed by teachers or students as it can be a
dreadful task to prepare for, which gives students pressure and as a result is not always the
most accurate reflection of learning. On the other hand, formative assessments have
advantages in a sense where it takes away the anxiety from students as these assessments are
not marked. It detaches the thinking that students must be correct at all times. Instead, they give
the teacher insight on their progress during normal lesson periods so they can assist them along
the way before they must take any summative assessments. Disadvantages of formative
assessment may include students failing to take them seriously, which may cause teachers to
misread feedback from students.
Callingham (2010) discusses that assessment is the most powerful element in teaching and
learning. For it to be helpful, it must be broad ranging, collecting a variety of information using a
range of tasks before, during and after a teaching sequence. There are both strengths and
weaknesses in each form of assessment, for example, summative assessment have many
advantages because they provide motivation to students to study and pay attention in class.
However, summative assessments are often not enjoyed by teachers or students as it can be a
dreadful task to prepare for, which gives students pressure and as a result is not always the
most accurate reflection of learning. On the other hand, formative assessments have
advantages in a sense where it takes away the anxiety from students as these assessments are
not marked. It detaches the thinking that students must be correct at all times. Instead, they give
the teacher insight on their progress during normal lesson periods so they can assist them along
the way before they must take any summative assessments. Disadvantages of formative
assessment may include students failing to take them seriously, which may cause teachers to
misread feedback from students.
References -
Callingham, R. (2010). Mathematics assessment in primary classrooms: Making it count.
Callingham, R. (2010). Mathematics assessment in primary classrooms: Making it count.
Kotzé, G. (2007). Investigating shape and space in mathematics: a case study. South African
Journal of Education, 27(1), 19-35.
Van, D. W. J. A., Karp, K. S., & Bay-Williams, J. M. (2015). Elementary and middle school
