Brown Samantha #17874739 Assessment 1 EDP343

Child study Report

Measurement and geometry

Completed by

Samantha Brown #17874739

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Brown Samantha #17874739 Assessment 1 EDP343

Contents

Introduction p. 3

Brief overview of diagnostic assessment p.4

Plan for teaching p.5

Explanation of tutoring sessions and specific mathematics taught p.5

Summary of what the child learnt p.11

What the child needs next p.11

Conclusion p.12

References p. 13

Appendixes p.14

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Brown Samantha #17874739 Assessment 1 EDP343

Introduction

This report examines the knowledge and understandings of a grade 3 student, in the area of

measurement and geometry specifically time measurement. This student will be identified as

Beth for the purpose of this report. The critical information explored throughout this report is

a brief overview of a one-on-one diagnostic assessment held with Beth surrounding

measurement and geometry strands of mathematics, focusing on the time measurement

section. Along with the initial plans for the first two tutoring sessions. A description of the

actual teaching sessions and the tasks and resources used and an explanation of why these

tasks were chosen for this child. Finally, a summary of what Beth learnt after the tutoring

sessions and a description of what the educator believes Beth needs next to further expand

the knowledge and understandings of these mathematical concepts.

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Brown Samantha #17874739 Assessment 1 EDP343

Brief overview of diagnostic assessment

Before the teacher begun the diagnostic assessment with Beth, an initial interview was

conducted with the mother. The interview held with the mother revealed the child struggles

with mathematics. The mother also stated that Beth finds it difficult when comprehending

time. After this discussion, the educator created a diagnostic assessment involving a variety

of areas of measurement and geometry with a focus on time measurement. The diagnostic

evaluation had 15 questions ranging from basic knowledge surrounding time to more probing

word problems. During the assessment, Beth became extremely nervous. Due to this Beth's

answers became erratic and Beth began to guess the answer rather than try and work the

problem through. For this reason, the educator decided to conduct a second assessment

held in the child’s home where Beth felt comfortable and safe.

The second evaluation revealed Beth's understanding of time lacks in depth. Beth's

responses to the questions exposed many misconceptions about time. Beth’s answers

showed a lack of knowledge surrounding specific terminology used within the assessment.

Reys, Lindquist, Lambdin, Smith, Rogers, Falle, Frid and Bennett (2012) state that students

require an in-depth understanding of the vocabulary used in determining time to grasp the

concepts of time thoroughly. Beth could not calculate or explain ideas surrounding half past

or quarter to on either an analogue clock or a digital clock. Booker, Bond, Sparrow and Swan

(2014) highlight the importance of fluency in computation as it is essential in developing a

student's confidence in using mathematics in different abstract circumstances. The

diagnostic assessment involved both an analogue and digital clocks and a wide variety of

questions relating to reading time and explaining how many minutes are in an hour and how

many seconds are in a minute. The information collected from the diagnostic interview

shows Beth's prior knowledge of time needs to be revisited to strengthen her abilities. The

Australian curriculum and reporting authority (ACARA) (2017) states, students at grade 3

level should be able to investigate the relationship between units of time and tell time to the

minute. Therefore this indicated that Beth needs to revisit the basics of time and clock

functions, revision of the language used in telling time, working with fractions and how the

hands move fractionally as the hour passes.

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Plan for teaching

After completing the diagnostic assessment with the child, the educator explored the

answers and explanations of the child to determine a starting point for several tutoring

sessions. Initially, the instructor planned two lessons for Beth as a way to further understand

her abilities and skills level. According to ACARA measurement and geometry (2017)

students should have knowledge of characteristics of quarter-past and half-past times and

be able to identify the features of a clock. The first meeting was constructed to revisit the

basics of time. As Beth struggled to understand the terminology used in the assessment and

how these terms related to numbers and fractions. The second session was also used to

compound Beth's knowledge of time vocabulary and relationships with numbers. Once the

child had gained a stronger understanding of the features of an analogue clock, the educator

decided to move forward and work on skip counting and five timetables; reading an

analogue clock and linking them to digital times, drawing the time on a clock without

numerals around the edges and using addition and subtraction procedures to find the correct

time within word problems.

Explanation of tutoring sessions and specific mathematics taught

Time is an abstract subject to learn, and the concept itself encapsulates an assortment of

cognitive skills that develop over their schooling experiences. Students need to have a

strong understanding of numbers from one to sixty along with the knowledge of skip counting

by fives, five timetables, counting on by ones, the direction of clock hands move,

understanding the terminology used and strong computation skills. Booker et al (2014)

explain students must draw upon their numeration theories, such as addition and subtraction

when telling units of time. Therefore, the educator decided to revisit concepts explored

during earlier years of Beth’s schooling. The first steps in mathematics: measurement book 1

(2013) explain students at this level should be able to describe the differences between

‘what time it is’ and ‘how much time it took’. As Beth cannot fully explain the features related

to time measurement it requires further development of the fundamentals of time

measurement.

As mentioned above, the initial tutoring session was designed to compound Beth's

knowledge of the features of an analogue clock. McMillen and Hernandez (2008) explain

that the traditional attitude to teaching students about time does not associate or highlight

the differences with the two hands of a clock. Therefore, the educator recognises the

importance of developing Beth's understanding of all the features of a clock for Beth to fully

grasp the concepts of time measurement. This session involved creating a clock face from

paper, see example one below. Beth then cut out the hands of the clock and labelled them

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Brown Samantha #17874739 Assessment 1 EDP343

according. Horak and Horak (1983) state that using an analogue clock face or slit clock

allows students to see what time come before and after a particular time. In using this

technique, it allows the student to see which direction the hands move in and builds on their

concepts of duration and the fractional movement of the hands. From this point, the educator

asked Beth questions related to each item, what the smaller hand represents, how many

minutes are in an hour and how many seconds are in a minute. Reys et at (2012) state

students must have an in-depth knowledge and be able to identify the hour and minute

hands and the direction they move in to tell time correctly. After this, Beth continued to

create the clock by adding the numerals around the edges. Once Beth had completed the

task, the educator asked Beth to use the hands to represent a variety of times. At this stage,

the teacher did not involve ideas surrounding the vocabulary that Beth did not understand

during the diagnostic assessment.

Example one Example two Example three

Therefore, the second lesson followed on from the previous session by asking reflective

questions about the features explored in the first lesson. Reys et al (2012) explain the

importance of using concrete materials and models when teaching students mathematics.

Therefore, using a slit clock gives Beth the context for the mathematical concept being

visited. Beth could break down the ideas explored previously and her responses to each

question were accurate and clear. During this session, the educator introduced the

vocabulary used when exploring time such as half-past, a quarter to and three quarters-past.

As shown in the picture below see example four, Beth was required to colour in fractional

sections amounting to minutes she thought each word represented. Beth struggled at first

with the idea that fractions are involved in telling/reading time. When asked what a quarter

past twelve is, Beth's response was "a quarter of what?" This showed the educator that Beth

did not recognise and understand that a clock has sixty minutes and between each numeral,

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Brown Samantha #17874739 Assessment 1 EDP343

there are four minutes. Horak and Horak (1983) explain that students need experiences

designed to acquaint them with standard fractional parts of an hour. From this point, the

educator decided to return to the clock that Beth created and work with fractions. This

exhibited to Beth that a clock is made up of sixty minutes and that she can skip count by

fives around the clock. The educator asked Beth questions such as, how many equal parts

can sixty be split into, what is half of sixty and what is a quarter of sixty. Beth could answer

these questions quite quickly once the knowledge that a clock is made up of sixty minutes

was realised.

Example four

The next lesson began with Beth explaining what she had learnt from the previous lessons

to ensure the knowledge surrounding the vocabulary used is strengthened. Thompson and

Van De Walle (1981) highlight the relevance of continuously reflecting and questing students

on pervious lessons to elicit responses relating to the concept being taught. During this

experience, the educator wanted to explore the importance of the numerals on a clock.

McMillen and Hernandez (2008) explain the relevance that the student recognises and

understands that the minute hand and its distance from the numeral twelve play a major

component in reading time correctly. As shown in the images below Beth's responses were

accurate see example five, six and seven. To reinforce the ideas explored in the second

session, the educator required Beth to draw the hands onto blank clocks. Thompson and

Van De Walle (1981) state students need to recognise that the hour hand moves a fractional

part of the distance from one hour number to the next. Beth exposed that she could

distinguish the meanings of the terminology used. Beth then begun to use different

strategies to work out where the hands were meant to go. The following are the procedures

Beth used, skip counting by 5s and counting on by ones. Reys et al (2012) explain how

students use time computation skills and mental mathematics in telling time. As Beth worked

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Brown Samantha #17874739 Assessment 1 EDP343

through the sheets shown below, she began to use strategies such as plus ten minus one to

place the minute hand on the clock. Beth was using mental mathematical strategies when

working through the worksheets. The educator realised that Beth could write the time on an

analogue clock without much difficulty at this point.

Example Five Example Six Example seven

Therefore, the instructor introduced a digital clock. First, the educator showed Beth a sheet

of digital clock times and asked her to tell the time. After this, the educator related these

times to the student's life and asked what she would be doing at certain times of the day.

Thompson and Van De Walle (1981) explain the procedure for telling time with a digital clock

is the same as telling time on an analogue clock. This activity allows Beth to identify the hour

on a digital clock as well as the minutes and how reading a digital clock references how

many minutes after the hour it is. The educator also asked Beth to use specific terminology

when repeating times. Beth read one digital clock as nine thirty. The educator asked if there

was another way of saying the time. Beth took time to respond to this question, but

responded with "it could be half past". The educator then asked another question "half past

when?" Beth responded with "whoops um nine". The teacher explained the importance of

being specific when answering questions related to time, as the answer must state what

hour it is to actually represent time. Booker et al (2014) indicate that students need to

recognise the different concepts of reading time from a digital clock to analogue. Although

the terminology is very similar, the way in which it is read are very different concepts. After

the discussion and exploration of digital clock times, the educator introduced a matching

game see examples eight, nine and ten. It requires the child to match the analogue clock to

the corresponding digital clock time. Beth worked through the matching sheet asking

questions to ensure the time was correct.

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Example eight Example nine Example ten

At the start of the fifth tutoring lesson the educator revisited all areas previously explored.

The instructor recognised that Beth's knowledge of time had expanded from the initial

diagnostic assessment and the educator decided to explore time phrases. Friederwitzer and

Berman (1999) examine the importance of recognising specific terminology used in telling

time, students need to understand fraction concepts and relate them to a circle shape when

telling time. The educator had a variety of time phrases in which the student was required to

write as a standard form. To help Beth with recognising the time phrases the educator gave

Beth the analogue clock made during the first session as a manipulative tool to use. Reys et

al (2012) state students need to gain a strong understanding of the language used when

telling time to grasp the passage of time concepts entirely. Having hands on items to use

when identifying the correct time phrases allowed Beth to correlate the correct answers. This

task requires Beth to explore the knowledge that was established during the previous

tutoring sessions with the terminology used to figure out the correct standard answers.

Thompson (2003) highlights the importance of having a strong prior knowledge of numerals

to use computation strategies. During this lesson, Beth also used skip counting by 5s to

figure out the answers. Example eleven shows the time phrase questions completed and

Beth’s answers written beside the question.

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Brown Samantha #17874739 Assessment 1 EDP343

Example Eleven

Coming to the end of the tutoring sessions the educator recognised the great strides Beth

had achieved during this time. Beth could identify and explain the terminology used when

reading time as well as making connections to skip counting on an analogue clock. During

the final two sessions, the educator wanted to explore word problems. Booker et al (2014)

explain students can devise appropriate standard algorithms and mental mathematic

strategies to determine the time. This activity introduces elapsed time and how simple

addition and subtraction algorithms are used to determine the correct time. The educator

used this tool to make the connection between other mathematical areas. Making

connections to addition, subtraction and multiplication skills will allow Beth to recognise

different ways to calculate time. See example twelve below for the activity sheet of word

problems. McMillen and Hernandez (2008) refers to these skills as computational methods

used in determining the time. This task was used to create connections between different

areas of mathematics that Beth can then use to work out time problems. Within example

twelve the answers were provided in the top section, but Beth was required to think of

strategies to use to make sure the chosen time was correct.

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Brown Samantha #17874739 Assessment 1 EDP343

Example Twelve

Summary of what the child learnt

After concluding the tutoring session, the educator recognised the improvements made. At

the start of the sessions, Beth was nervous and guessed most of the answers as the prior

knowledge of the child was undeveloped. During the sessions, a lot of conversations

happened before, during and after the sessions to reiterate what mathematics concepts

were explored. This was done continuously to involve reflective and critical thinking skills.

After the first three lessons Beth’s knowledge of an analogue clock and its features was

strengthened to the point where Beth could move forward to different areas. These included

reading time, writing time on a clock, reading a digital clock and using specific terminology

related to time, matching digital clock times to analogue clock times and using mathematical

strategies such as skip counting, add ten minus one technique, five timetables and addition

and subtraction algorithms to work out worded problems.

What the child needs next

Therefore, the knowledge Beth has developed over the seven tutoring sessions has

strengthened her prior knowledge of time measurement. From this point, Beth needs to

revisit ideas surrounding the relationships between units of time to progress forward and

make connections to the operations for converting units of time.

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Conclusion

Finally, this report explored the knowledge and abilities held by an eight-year-old student

based on a diagnostic interview of time measurement. Then the educator identified that

Beth required a stronger basic understanding of time and the different functions and

components of a clock to progress any further. Thus, the educator explores ideas

surrounding an initial starting point for the several tutoring session. This report examines the

progression made from the initial assessment to the end of the sessions. To conclude, the

educator reflects on the experiences and achievements of the child and determines that

Beth requires a deeper understanding of converting units of time to further develop

understandings of time measurement for the future.

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Brown Samantha #17874739 Assessment 1 EDP343

References

Australian Curriculum and Reporting Authority. (2017). Measurement and geometry year 3. Retrieved from http://www.australiancurriculum.edu.au/mathematics/curriculum/f-10?y=2&y=3&y=4&s=MG&layout=1

Booker, G., Bond, D., Sparrow, L., & Swan, P. (2014). Teaching Primary Mathematics 5th edition. Pearson Australia. French Forest

Department of Education. (2013).First steps in Mathematics: Measurement Book 1. Retrieved from file:///C:/Users/Samantha/Downloads/FIRST013%20(1).pdf

Friederwitzer, F. & Berman, B. (1999). The language of time. Retrieved from

http://www.jstor.org.dbgw.lis.curtin.edu.au/stable/pdf/41197403.pdf

Horak, V.M. & Horak, W.J. (1983). Teaching time with slit clocks. Retrieved from

http://www.jstor.org.dbgw.lis.curtin.edu.au/stable/pdf/41192158.pdf

McMillen, S. & Herandez, B.O. (2008).Teaching children mathematics: Teaching time to

understand telling time. Retrieved from

http://maccss.ncdpi.wikispaces.net/file/view/Taking+Time+to+Understand+Time.pdf

Reys, E., Lindquist M., Lambdin, D., Smith, N., Rogers, A., Falle, J., Frid, S & Bennett, S. (2012). Helping children learn mathematics. John Wiley & Sons Australia, Ltd

Thompson, C. S., & Van De Walle, J. (1981). A single handed approach to telling time.

Retrieved from http://www.jstor.org.dbgw.lis.curtin.edu.au/stable/pdf/41191860.pdf

Thompson, I. (2003). Enhancing primary mathematics teaching. Retrieved from

http://ebookcentral.proquest.com.dbgw.lis.curtin.edu.au/lib/curtin/reader.action?

docID=295497

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Appendixes

1.0 Parent letter

1.1. Tutoring session log

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