ISSUE - Years 1-3 students having difficultly telling the time with the use of the correct terminology (half past, quarter past and quarter to) for digital and analogue clocks. (Measurement and Geometry strand and sub-strand of Units of Measurement)
The issue of not being able to tell or read either digital or analogue time is a real distress for any human being. Reading the time “helps develop important abstract, perceptual, and cognitive skills badly needed in a modern, digital world”. (Massaro, Kid Klok, 1991) The whole world revolves around what the time is. “The concept of time is something that young students face daily, for example, hurrying to get to school or getting to stay up late”. (Siemon, et al., 2011, p. 449) Life depends on time; what time to start work, what time school starts, what time the shops open to get groceries. Being able to tell/read the time is an essential skill that must be taught and learnt clearly and correctly to students throughout the younger years of the student’s educational experiences. There are a range of possible origins that relate to the issue of telling/reading time. These include connection with number sense, place value, fractions, length, spatial awareness and knowledge of terminology.
The mathematical knowledge required to tell the time connects with many mathematical strands and sub-strands within the Australian Mathematics Curriculum. Being able to tell the time has a direct connection to English literacy with the inclusion of the comprehension of mathematical terminology used. The language concern of these issues effects the student’s mathematical capabilities as knowledge of time terminology requires “further development of mathematical ideas and competencies which depend on a large extent of the development of language appropriate to the task in hand”. (Siemon, et al., 2011, p. 276) If students don’t understand nor connect with the appropriate terminology, for example ‘big hand’ or ‘little hand’ they will not be able to comprehend the required knowledge and therefore won’t be able to tell the time in either digital or analogue form.
Students also need to connect and comprehend the language used when teaching time such as before and after, up and down, and left and right. Knowledge of this terminology connects the student’s spatial awareness which is an essential learning key for telling the time. ”A great deal of spatial skill is required in order to understand concepts like place, value, signs, borrowing and division. Time is spatial; it requires an understanding of ordered sequences.” (Society, 2012)
Time is included in the Units of Measurement sub-strand of the Measurement and Geometry section of the Australian Mathematics Curriculum. The Measurement and Geometry strand focuses on increasing the student’s mathematical knowledge in regards to “understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three-dimensional objects of space” (ACARA, 2012) across the years. “The measurement of length and time are foundational components of measurement learning in the early years”. (Siemon, et al., 2011, p. 452) “The measurement of length takes a central position in the primary measurement curriculum because an understanding of length is essential to building other measurement concepts”. (Siemon, et al., 2011, p. 452)
The Units of Measurements sub-strand for time focuses on the following; Year 1 -Tell time to the half hour (ACMMG020) -Reading time on analogue and digital clocks and observing the characteristics of half hour times Year 2 -Tell time to the quarter hour, using the language of 'past' and 'to' (ACMMG039) -Describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three Year 3 -Tell time to the minute and investigate the relationship between units of time (ACMMG062) -Recognising there are 60 minutes in an hour and 60 seconds in a minute (ACARA, 2012) Mathematical learning for students in lower primary year’s impacts on the student’s Number and Algebra learning through fractions and decimals and the Number and Place Value sub-strands of the Australian Mathematics Curriculum. The Number and Algebra strand develops the student’s ability to “apply number sense and strategies for counting and representing numbers”. (ACARA, 2012) It also allows the students “understanding of the number system to describe relationships and formulate generalisations by conducting investigations, problem solving tasks and the ability to communicate their reasoning”. (ACARA, 2012)
The first issue students may have in regards to understanding time links directly to the sub-strand of Number and Place Value. This issue requires the students recognise the numbers from zero to nine. It is stated that “the whole number 0 to 9 are the only numbers most of us ever need to know, as every other number we routinely come across is made up of some combination of these numbers in accordance with accepted patterns such as place value”. (Siemon, et al., 2011, p. 279) The inability to recognise numbers zero to nine decreases the student’s ability to state the time represented on the clock in the appropriate manner. For example, if the student cannot recognise the number four they will not be able to state that the time is half-past four. In regards to time, students must have the ability and knowledge to recognise the numbers between one and twelve which are represented in analogue form and number between one and twenty-four which are represented in digital form. Students need this recognition ability to connect with the ordering/sequencing/positioning of the numbers on the clock face. For example, students need to know to read the numbers on the clock in a clockwise direction.
The second issue students may face is not having a well established understanding of place value within the number system. “Place value is one of the ‘big ideas’ needed to develop a deep understanding of numbers”. (Siemon, et al., 2011, p. 317) Students must understand and comprehend the role of place value in a number sense to continue with any number that is higher than nine. In relation to telling the time students must be able to use their number sense and place value knowledge from zero to sixty. Students must also have the ability to count from zero to sixty in order to assist their ability to tell and represent various times.
When viewing the issue of counting from zero to sixty students require a sense of number beyond ten. Students need an understanding of their place value knowledge to connect that fifteen minutes is represented in a number sense as 1 tens and 5 ones, which then equals fifteen minutes or a quarter of an hour. This knowledge is essential for the students to have when telling the time and for understanding the various time terminologies used when reading the time. Students must have extensively experienced this knowledge as “this understanding is developed later when experiencing number more effectively by counting in two’s, fives and ultimately tens” (Siemon, et al., 2011) which is required when reading the time with the use of various time terminology. For example this knowledge must be used and understood by the students to state that the time is ten minutes past three O’clock, by counting in fives on the clock face. Also with this knowledge students can connect with the length value of time. For example, sixty seconds equals one minute and sixty minutes equals one hour. This knowledge is essential for the student to be able to connect and represent various times with the use of different terminology to tell the time.
Another issue is that students don’t connect with the duration of time. For example they don’t clearly understand that “brushing my teeth is shorter than eating breakfast, which is shorter than walking to school”. (Siemon, et al., 2011, p. 449) In connection to this the students do not have any relation to the passing or sequence of time in regards to the division of days, and weeks. Without this knowledge students have minimal association with “broad daily partitions, such as morning, afternoon, and night which are introduced with the relationship between successive days, that is yesterday, today, and tomorrow” (Siemon, et al., 2011, p. 449) which decreases the student’s ability to be able to connect directly with basic time lengths. This affects the student’s ability to be able to tell the time by having an unestablished relationship between shorter and longer lengths of time which leads to an unestablished relationship between seconds and minutes and minutes and hours.
This issue can be supported by connection to times of the day, time periods and units of time. Students need to have this knowledge because “when the three board divisions of morning, afternoon, and night have been grasped, the idea that the day can be divided further can be introduced” through the “investigation of standards units of second, minute, and hour which develops some understanding of how long these units are” (Siemon, et al., 2011, p. 450) This knowledge then links to the student being able to make comparisons between sixty seconds and one minute, sixty minutes and one hour, thirty minutes and half an hour etc. This is essential in being able to tell the time with the use of various terminologies. For example, thirty minutes past six or half-past six.
Another issue that affects the student’s ability to tell the time using the correct terminology is in relation to fractions. This connects directly to the fractions and decimals sub-strand within the Number and Algebra strand of the Australian Mathematics Curriculum. If students don’t have the ability to recognise what a quarter of a particular shape is, they will not be able to visualise and connect with the time terminology of quarter past and quarter to associated with telling the time. This is seen as an issue because students require the ability to know and recognise half, quarters and whole to clearly associate with the time terminology used. For example half-past five, quarter-to eight and quarter-past two.
The varying terminology used to tell the time (either digital or analogue) can be quiet confusing for a student to grasp. The time terminology of ‘quarter-to’ and ‘quarter-past’ directly links time to the fractions component of mathematics. If the students don’t have an understanding of fractions the terminology used to represent quarter to seven which could be misinterpreted by the students because of the lack of fraction knowledge and understanding.
Another issue is that time is represented in a range of ways (written, spoken, visual) which the students have to try and visualise, connect, understand and represent the time from. The different terminology that is used when telling the time is represented as an issue that could affect the student’s ability to read and tell the time (both digital or Analogue time and also digital time in 24 hours) later in life as reading the time “helps develop important abstract, perceptual, and cognitive skills badly needed in a modern, digital world” (Massaro, Kid Klok, 1991)and time evolves the world around everyone.
The issue of not being able to tell or read either digital or analogue time is a real distress for any human being. Reading the time “helps develop important abstract, perceptual, and cognitive skills badly needed in a modern, digital world”. (Massaro, Kid Klok, 1991) The whole world revolves around what the time is. “The concept of time is something that young students face daily, for example, hurrying to get to school or getting to stay up late”. (Siemon, et al., 2011, p. 449) Life depends on time; what time to start work, what time school starts, what time the shops open to get groceries. Being able to tell/read the time is an essential skill that must be taught and learnt clearly and correctly to students throughout the younger years of the student’s educational experiences. There are a range of possible origins that relate to the issue of telling/reading time. These include connection with number sense, place value, fractions, length, spatial awareness and knowledge of terminology.
The mathematical knowledge required to tell the time connects with many mathematical strands and sub-strands within the Australian Mathematics Curriculum. Being able to tell the time has a direct connection to English literacy with the inclusion of the comprehension of mathematical terminology used. The language concern of these issues effects the student’s mathematical capabilities as knowledge of time terminology requires “further development of mathematical ideas and competencies which depend on a large extent of the development of language appropriate to the task in hand”. (Siemon, et al., 2011, p. 276) If students don’t understand nor connect with the appropriate terminology, for example ‘big hand’ or ‘little hand’ they will not be able to comprehend the required knowledge and therefore won’t be able to tell the time in either digital or analogue form.
Students also need to connect and comprehend the language used when teaching time such as before and after, up and down, and left and right. Knowledge of this terminology connects the student’s spatial awareness which is an essential learning key for telling the time. ”A great deal of spatial skill is required in order to understand concepts like place, value, signs, borrowing and division. Time is spatial; it requires an understanding of ordered sequences.” (Society, 2012)
Time is included in the Units of Measurement sub-strand of the Measurement and Geometry section of the Australian Mathematics Curriculum. The Measurement and Geometry strand focuses on increasing the student’s mathematical knowledge in regards to “understanding of size, shape, relative position and movement of two-dimensional figures in the plane and three-dimensional objects of space” (ACARA, 2012) across the years. “The measurement of length and time are foundational components of measurement learning in the early years”. (Siemon, et al., 2011, p. 452) “The measurement of length takes a central position in the primary measurement curriculum because an understanding of length is essential to building other measurement concepts”. (Siemon, et al., 2011, p. 452)
The Units of Measurements sub-strand for time focuses on the following;
Year 1
- Tell time to the half hour (ACMMG020)
- Reading time on analogue and digital clocks and observing the characteristics of half hour times
Year 2
- Tell time to the quarter hour, using the language of 'past' and 'to' (ACMMG039)
- Describing the characteristics of quarter past times on an analogue clock, and identifying that the small hand is pointing just past the number and the big hand is pointing to the three
Year 3
- Tell time to the minute and investigate the relationship between units of time (ACMMG062)
- Recognising there are 60 minutes in an hour and 60 seconds in a minute
(ACARA, 2012)
Mathematical learning for students in lower primary year’s impacts on the student’s Number and Algebra learning through fractions and decimals and the Number and Place Value sub-strands of the Australian Mathematics Curriculum. The Number and Algebra strand develops the student’s ability to “apply number sense and strategies for counting and representing numbers”. (ACARA, 2012) It also allows the students “understanding of the number system to describe relationships and formulate generalisations by conducting investigations, problem solving tasks and the ability to communicate their reasoning”. (ACARA, 2012)
The first issue students may have in regards to understanding time links directly to the sub-strand of Number and Place Value. This issue requires the students recognise the numbers from zero to nine. It is stated that “the whole number 0 to 9 are the only numbers most of us ever need to know, as every other number we routinely come across is made up of some combination of these numbers in accordance with accepted patterns such as place value”. (Siemon, et al., 2011, p. 279) The inability to recognise numbers zero to nine decreases the student’s ability to state the time represented on the clock in the appropriate manner. For example, if the student cannot recognise the number four they will not be able to state that the time is half-past four. In regards to time, students must have the ability and knowledge to recognise the numbers between one and twelve which are represented in analogue form and number between one and twenty-four which are represented in digital form. Students need this recognition ability to connect with the ordering/sequencing/positioning of the numbers on the clock face. For example, students need to know to read the numbers on the clock in a clockwise direction.
The second issue students may face is not having a well established understanding of place value within the number system. “Place value is one of the ‘big ideas’ needed to develop a deep understanding of numbers”. (Siemon, et al., 2011, p. 317) Students must understand and comprehend the role of place value in a number sense to continue with any number that is higher than nine. In relation to telling the time students must be able to use their number sense and place value knowledge from zero to sixty. Students must also have the ability to count from zero to sixty in order to assist their ability to tell and represent various times.
When viewing the issue of counting from zero to sixty students require a sense of number beyond ten. Students need an understanding of their place value knowledge to connect that fifteen minutes is represented in a number sense as 1 tens and 5 ones, which then equals fifteen minutes or a quarter of an hour. This knowledge is essential for the students to have when telling the time and for understanding the various time terminologies used when reading the time. Students must have extensively experienced this knowledge as “this understanding is developed later when experiencing number more effectively by counting in two’s, fives and ultimately tens” (Siemon, et al., 2011) which is required when reading the time with the use of various time terminology. For example this knowledge must be used and understood by the students to state that the time is ten minutes past three O’clock, by counting in fives on the clock face. Also with this knowledge students can connect with the length value of time. For example, sixty seconds equals one minute and sixty minutes equals one hour. This knowledge is essential for the student to be able to connect and represent various times with the use of different terminology to tell the time.
Another issue is that students don’t connect with the duration of time. For example they don’t clearly understand that “brushing my teeth is shorter than eating breakfast, which is shorter than walking to school”. (Siemon, et al., 2011, p. 449) In connection to this the students do not have any relation to the passing or sequence of time in regards to the division of days, and weeks. Without this knowledge students have minimal association with “broad daily partitions, such as morning, afternoon, and night which are introduced with the relationship between successive days, that is yesterday, today, and tomorrow” (Siemon, et al., 2011, p. 449) which decreases the student’s ability to be able to connect directly with basic time lengths. This affects the student’s ability to be able to tell the time by having an unestablished relationship between shorter and longer lengths of time which leads to an unestablished relationship between seconds and minutes and minutes and hours.
This issue can be supported by connection to times of the day, time periods and units of time. Students need to have this knowledge because “when the three board divisions of morning, afternoon, and night have been grasped, the idea that the day can be divided further can be introduced” through the “investigation of standards units of second, minute, and hour which develops some understanding of how long these units are” (Siemon, et al., 2011, p. 450) This knowledge then links to the student being able to make comparisons between sixty seconds and one minute, sixty minutes and one hour, thirty minutes and half an hour etc. This is essential in being able to tell the time with the use of various terminologies. For example, thirty minutes past six or half-past six.
Another issue that affects the student’s ability to tell the time using the correct terminology is in relation to fractions. This connects directly to the fractions and decimals sub-strand within the Number and Algebra strand of the Australian Mathematics Curriculum. If students don’t have the ability to recognise what a quarter of a particular shape is, they will not be able to visualise and connect with the time terminology of quarter past and quarter to associated with telling the time. This is seen as an issue because students require the ability to know and recognise half, quarters and whole to clearly associate with the time terminology used. For example half-past five, quarter-to eight and quarter-past two.
The varying terminology used to tell the time (either digital or analogue) can be quiet confusing for a student to grasp. The time terminology of ‘quarter-to’ and ‘quarter-past’ directly links time to the fractions component of mathematics. If the students don’t have an understanding of fractions the terminology used to represent quarter to seven which could be misinterpreted by the students because of the lack of fraction knowledge and understanding.
Another issue is that time is represented in a range of ways (written, spoken, visual) which the students have to try and visualise, connect, understand and represent the time from. The different terminology that is used when telling the time is represented as an issue that could affect the student’s ability to read and tell the time (both digital or Analogue time and also digital time in 24 hours) later in life as reading the time “helps develop important abstract, perceptual, and cognitive skills badly needed in a modern, digital world” (Massaro, Kid Klok, 1991)and time evolves the world around everyone.