Inquiry in the Mathematics Classroom Assignment

Assignment Task

For this assessment you must work with a suitable child and determine what they know about the topic of Measurement, gather evidence about their understandings and misunderstandings, provide interventions that assist the child to improve and write a report about the experience in a professional style.

In preparation for the assessment, ensure you have current “working with children” certification valid for your educational jurisdiction. For example, in Western Australia this is the “Working With Children Card” and in Queensland it is the “Blue Card”. A copy of this document must be included as an appendix in your uploaded assessment. Check that your certification has not expired and will not expire during the period of the intervention. A receipt for application to renew the certification is sufficient to be able to start the assessment - but check this is satisfactory for parents or the school where you are working with the child. Also include as appendices with the submission scanned or photographed copies of the (signed) Parent or Teacher or Principal Permission Form and the (signed) Tutoring Log. Ensure the email address of the Parent or Teacher or Principal is legible.

The topic of Measurement is particularly important in Year 3, Year 4 and Year 5. The child for your Child Study must be in one of those school years. A Year 3 child who is particularly able with Measurement, or a Year 5 child who struggles with the topic, are suitable. For particularly able children, the Child Study can venture into the topic of Area - see the alternative Advanced section below.

Measurement is covered in Chapter 19 of the Van de Walle et al. textbook (all Australian editions). Citations here are by section, rather than by page number, and year of publication is not cited in-text here so that either the 1st Australian edition or the 2nd Australian edition of Van de Walle et al. can be used. Ensure that you have thorough familiarity with this resource and with the appropriate parts of the mathematics curriculum current in your jurisdiction, including the elaborations.

Measurement is covered in Chapter 19 of the Van de Walle et al. textbook (all Australian editions). Citations here are by section, rather than by page number, and year of publication is not cited in-text here so that either the 1st Australian edition or the 2nd Australian edition of Van de Walle et al. can be used. Ensure that you have thorough familiarity with this resource and with the appropriate parts of the mathematics curriculum current in your jurisdiction, including the elaborations.

Conducting the Diagnostic

Conducting the Diagnostic Assessment Interview It is vital that you read these guidelines from start to finish before working with your child subject.

Ensure that your interactions with the child and their parents and teachers are professional at all times. Be thoroughly prepared and have a range of tasks and resources ready. Interview responses from children are not necessarily what you would expect. You may or may not use all of the tasks, questions, and prompts suggested here. They exist to cover a wide range of possibilities. They may be supplemented with materials from other academic sources, the curriculum elaborations, Mathspace and similar high quality published Australian teacher resources - but not random ideas from the internet.

Measurement is the focus for this assessment, in particular, the attributes of length and possibly area if the child demonstrates a very strong conceptual understanding of length. Other attributes may be explored if a child shows very strong understanding of length and area. Experience shows that this is unlikely.

The attributes of length and area are reasonably accessible and resources are relatively easy to provide. Also, if used, area is a good choice because the use of non-standard units is sometimes under-emphasised with older children. Non-standard units should initially be used to measure irregular shapes, enabling children to focus on the attribute and not the unit. The initial diagnostic tools for this assessment are summarised below. You should have a variety of resources with you, such as pen and paper, toothpicks, pop-sticks, tiles, counters, paper clips, string, 30cm ruler, small measuring tape, grid paper of different sizes, and a few small objects to measure.

Drinking straws are useful because they can be cut to length and can be threaded on a string. Use your phone to record the sessions so that you can transcribe exactly what the child said, and take photographs of the work produced by the child (not photographs of the child). Be attentive to what the child actually conveys, do not just listen for the answers you expect! Ensure you have eye contact so that you can also note indications of confidence in the child.

Interview tasks for Structure Point

1. Identification and understanding of the attribute

Children do not necessarily have a sound understanding of what a length is, nor what it is used for. Is width, height, depth, thickness, perimeter, circumference or distance a “length”? Have a conversation with the child subject and explore what their understandings are.

Questions

1. How would you describe what length means?

2. How would you measure the length of this line (curly line)?

3. Can you measure it? How would you find out exactly how long something is?

4. Can you show me where the length of this table is?

5. To test understanding, indicate the width of the table and ask, ‘Could this be the length?’

6. Then ask, ‘Does it matter which one we choose?’

7. How would you measure the length of this table?

8. Change the orientation of an object (e.g., stand it up on its end). Ask, ‘Has the length changed?’ Explore the language around the concept of height, length, width, depth. Use a rectangular object such as a book. Ask ‘What is the length and width?’

9. Then rotate the book by 90 degrees. Ask, ‘Now what is the length and the width?’ ‘Have they changed?’

10. Use an ice cream container, or similar. Ask, ‘What is the depth?’ and ‘Is it the same as length?’ Another good question to use would be to show the child a container (ice cream tub, small bucket, box etc.) and ask the child to ‘measure it’. Facilitate a discussion about ‘what to actually measure’ to see what knowledge the child has about attributes that could be measured.

2. Compare and order objects

Ask the child to arrange a set of objects in order. For example, provide 4 or 5 pictures or models of fish that are very close in length and have different widths

1. How do you know if something is longer than something else?

2. Is it the same as asking ‘How do you know if something is bigger than something else?’ Use open questions like ‘

3. What can you tell me about these two objects?’ Activity 19.7 in Van de Walle et al. “Length (or unit) hunt” may be useful.

4. You will need to note which type of comparison the child uses. It could be one of the following: 

5. Perceptual comparison, such as looking at two objects and stating which one is longer.

6. Direct comparison, by placing one alongside the other.

7. Indirect comparison, by using another object such as a piece of string to compare two objects that cannot be physically moved next to one another.

3. Direct Measure with informal units

Ask the subject child to compare two straight lines drawn at angles to each other on a page.

• How can they be sure which one is the longest? Encourage the child to use body parts such as finger widths. Activity 19.6 in Van de Walle et al. “Longer, shorter, same” and Activity 19.7 “Length (or unit) hunt” may be useful. When objects are not straight, comparison is an entirely new challenge.
• Use two pieces of string or draw curved lines on a page or chalk them on a pavement. How does the child compare their lengths? Activity 19.8 in Van de Walle et al. “Crooked paths” may be useful.
• Ask the child to measure something that is reasonably small (e.g., a small toy car) with a piece of string about one metre long.
• Observe what the child does. Facilitate a conversation about needing a smaller unit.

4. Direct Measure with standard units

• Have the child estimate before moving on to make actual measurements. Ask how they made their estimation.
• Start with Van de Walle et al. Activity 19.10 on “Estimate and measure” and follow up with the questions posed in the following “Formative Assessment” section. Follow-up questions such as these could be used:
• Ask the child to measure a particular object with two different units or two different ways. Predict. Can you explain why the measurements are different?
• Facilitate a discussion about the smaller the unit, the more of them will be needed. Perhaps use pop-sticks and toothpicks or paper clips. Ask the child to measure using the pop-sticks and then paper clips. Ask, ‘Is there another way you could have done that, without measuring with both units?’
• The aim is to see if the child can compare the two units first and make an estimation based on that. Activity 19.13 in Van de Walle et al. “Make your own ruler” is a good task to reinforce the idea that it is the number of spaces on the instrument and not the number of calibration marks that are important.
• Children can compare their ruler with standard rulers. The “broken ruler” task shown in Figure 1 is designed to test whether a student understands the attribute of measurement, not just the process of measuring.

5. Apply measurement to everyday contexts, including estimation and indirect measure

• Do you think this table would fit through that doorway?
• How far is it between your home and your school? 
• Is the school boundary a length or an area?

Advanced Diagnostic Interview With Focus on Area

This diagnostic interview is only used if the child is clearly proficient with the topic of Length. Use some activities from the Standard Diagnostic Interview above to check that the child is confident and correct with Length.

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