In Hoerl & McCormack's (H&M's) dual-systems approach, infants and very young children rely on a temporal updating system to change representations over time, but older children develop a more mature temporal reasoning system that allows for representation of change. Although this developmental account is consistent with findings from our research on children's temporal understanding, H&M do not explain the processes leading to this shift.
Evidence for young children's use of a temporal updating system comes from our research indicating that young children are consistently better at forward temporal thinking than backward temporal thinking. We tested 3- to 5-year-olds’ understanding of yesterday and tomorrow with a picture-selection task in which children heard sentences such as, “I carved the pumpkin yesterday,” and were asked, “What does it look like now?” (Zhang & Hudson Reference Zhang and Hudson2018a). Answering this question involves thinking forward from yesterday to today. However, children could also respond correctly by simply updating their representation of the pumpkin from an intact pumpkin to a carved pumpkin without considering the temporal relationship between yesterday and today. In contrast, children were less accurate when backward thinking was required, as when they heard the sentence, “I'm gonna carve the pumpkin tomorrow,” and were asked, “What does it look like now?” To answer this question correctly, children needed to represent the change as occurring at a future time point and temporally de-center between the future point and the present; this requires a temporal reasoning system. Hence, children could rely on a temporal updating system to solve forward reasoning problems, but not backward reasoning problems.
Superior performance in forward thinking was observed across several temporal understanding tasks: In English-speaking and Mandarin-speaking children (Zhang & Hudson Reference Zhang, Hudson and Hudson2018b); in tasks involving change in possession as well as change in physical states (Zhang Reference Zhang2019); and in a simpler task in which children were asked questions such as, “What did the pumpkin look like before I carved it?” or “What will the pumpkin look like after I carve it?” (Zhang & Hudson Reference Zhang and Hudson2018a). Tasks using spatial cues to test children's understanding of the sequential relations between time points such as yesterday, today, and tomorrow also elicited more errors in backward problem solving (Zhang Reference Zhang2019). These findings support the view that young children can solve problems that involve temporal updating before they are capable of temporal reasoning.
This shift from temporal updating to temporal reasoning is a critical developmental achievement. However, it is unclear what happens early in development that prepares children for the ability to reason about time at 4 to 5 years of age. We propose that development proceeds from representing change as ordinal updates (i.e., “and then, and then, and then”), to ordinal representation in the form of before-after relations between units within events, to interval measurement with event-independent measurement units (e.g., days), to the ratio measurement involved in the clock and calendar systems.
The mature adult conception of “common time” is linear, unidirectional, event independent, and unified; it is a common conception among humans and is common to all changes (McCormack & Hoerl Reference McCormack and Hoerl2017). Children's awareness of before-and-after states of change is the beginning of their construction of common time. When children grasp the relationship between an initially intact block tower and a fallen block tower as before and after (without necessarily using the linguistic expressions “before” and “after”), they engage in ordinal representation. They then expand the scope of the units considered in this relation: from states (e.g., toothbrush on counter-toothbrush in hand), to actions or events (e.g., bathing-teeth brushing) to event sequences (e.g., bedtime routine).
Expanding the scope of the ordered units from actions within events to events within a day is difficult because there is variability in daily event chains. For example, on some days, there is a car ride to preschool following the morning routine of getting up, dressing, and having breakfast, but on other days, this car ride does not follow. When children notice the recurring pattern of event sequences in a day, they can chunk the “day” as a unit, and place days in a before-and-after relationship. The day is a universal unit of change, easily observable by the astronomical light-dark cycle and demarcated for children by going to bed and getting up. This is still ordinal representation. The relationship between yesterday, today, and tomorrow is an ordinal one. However, once the ordered unit has reached the event-independent “day,” using this unit for interval measurement is not a big leap, for example, “two days.” The grasp of the unit “day” is a prerequisite for understanding the week and the other units of the calendar system. It is the repetition of temporal measurement units that gives a cyclical aspect to linear common time.
In our research with 3- to 6-year-olds, we found that irrespective of age, children with richer scripts for event sequences in the day were better at ordering pictures of events in the day, naming the parts of the day, naming the days of the week, and naming the day before Wednesday. Better receptive vocabulary and pattern reasoning ability were also related to more extensive scripts (Mayhew & Hudson Reference Mayhew and Hudson2017; Mayhew Reference Mayhew and Hudson2018).
These findings not only offer evidence for the connection between elaborate representations of event sequences in the day and the ability to consider the day as a unit, but also point to the importance of other cognitive skills in the development of temporal reasoning. Memory skills are necessary for chunking the day as a unit; numeracy skills are needed for interval measurement of duration; pattern reasoning skills facilitate observation of recurrent event sequences; and language skills are needed to map words to observed temporal relationships.
In our view, the temporal updating system, with its sensitivity for ordered sequences, bootstraps the temporal reasoning system by furnishing the “and then, and then, and then” sequences where before-and-after relations can be noticed. Children's expanding event representations, along with developments in language and other cognitive competencies, provide the foundation for reasoning about temporal sequence. It is these developments that enable the shift from the temporal updating system to the temporal reasoning system.
In Hoerl & McCormack's (H&M's) dual-systems approach, infants and very young children rely on a temporal updating system to change representations over time, but older children develop a more mature temporal reasoning system that allows for representation of change. Although this developmental account is consistent with findings from our research on children's temporal understanding, H&M do not explain the processes leading to this shift.
Evidence for young children's use of a temporal updating system comes from our research indicating that young children are consistently better at forward temporal thinking than backward temporal thinking. We tested 3- to 5-year-olds’ understanding of yesterday and tomorrow with a picture-selection task in which children heard sentences such as, “I carved the pumpkin yesterday,” and were asked, “What does it look like now?” (Zhang & Hudson Reference Zhang and Hudson2018a). Answering this question involves thinking forward from yesterday to today. However, children could also respond correctly by simply updating their representation of the pumpkin from an intact pumpkin to a carved pumpkin without considering the temporal relationship between yesterday and today. In contrast, children were less accurate when backward thinking was required, as when they heard the sentence, “I'm gonna carve the pumpkin tomorrow,” and were asked, “What does it look like now?” To answer this question correctly, children needed to represent the change as occurring at a future time point and temporally de-center between the future point and the present; this requires a temporal reasoning system. Hence, children could rely on a temporal updating system to solve forward reasoning problems, but not backward reasoning problems.
Superior performance in forward thinking was observed across several temporal understanding tasks: In English-speaking and Mandarin-speaking children (Zhang & Hudson Reference Zhang, Hudson and Hudson2018b); in tasks involving change in possession as well as change in physical states (Zhang Reference Zhang2019); and in a simpler task in which children were asked questions such as, “What did the pumpkin look like before I carved it?” or “What will the pumpkin look like after I carve it?” (Zhang & Hudson Reference Zhang and Hudson2018a). Tasks using spatial cues to test children's understanding of the sequential relations between time points such as yesterday, today, and tomorrow also elicited more errors in backward problem solving (Zhang Reference Zhang2019). These findings support the view that young children can solve problems that involve temporal updating before they are capable of temporal reasoning.
This shift from temporal updating to temporal reasoning is a critical developmental achievement. However, it is unclear what happens early in development that prepares children for the ability to reason about time at 4 to 5 years of age. We propose that development proceeds from representing change as ordinal updates (i.e., “and then, and then, and then”), to ordinal representation in the form of before-after relations between units within events, to interval measurement with event-independent measurement units (e.g., days), to the ratio measurement involved in the clock and calendar systems.
The mature adult conception of “common time” is linear, unidirectional, event independent, and unified; it is a common conception among humans and is common to all changes (McCormack & Hoerl Reference McCormack and Hoerl2017). Children's awareness of before-and-after states of change is the beginning of their construction of common time. When children grasp the relationship between an initially intact block tower and a fallen block tower as before and after (without necessarily using the linguistic expressions “before” and “after”), they engage in ordinal representation. They then expand the scope of the units considered in this relation: from states (e.g., toothbrush on counter-toothbrush in hand), to actions or events (e.g., bathing-teeth brushing) to event sequences (e.g., bedtime routine).
Expanding the scope of the ordered units from actions within events to events within a day is difficult because there is variability in daily event chains. For example, on some days, there is a car ride to preschool following the morning routine of getting up, dressing, and having breakfast, but on other days, this car ride does not follow. When children notice the recurring pattern of event sequences in a day, they can chunk the “day” as a unit, and place days in a before-and-after relationship. The day is a universal unit of change, easily observable by the astronomical light-dark cycle and demarcated for children by going to bed and getting up. This is still ordinal representation. The relationship between yesterday, today, and tomorrow is an ordinal one. However, once the ordered unit has reached the event-independent “day,” using this unit for interval measurement is not a big leap, for example, “two days.” The grasp of the unit “day” is a prerequisite for understanding the week and the other units of the calendar system. It is the repetition of temporal measurement units that gives a cyclical aspect to linear common time.
In our research with 3- to 6-year-olds, we found that irrespective of age, children with richer scripts for event sequences in the day were better at ordering pictures of events in the day, naming the parts of the day, naming the days of the week, and naming the day before Wednesday. Better receptive vocabulary and pattern reasoning ability were also related to more extensive scripts (Mayhew & Hudson Reference Mayhew and Hudson2017; Mayhew Reference Mayhew and Hudson2018).
These findings not only offer evidence for the connection between elaborate representations of event sequences in the day and the ability to consider the day as a unit, but also point to the importance of other cognitive skills in the development of temporal reasoning. Memory skills are necessary for chunking the day as a unit; numeracy skills are needed for interval measurement of duration; pattern reasoning skills facilitate observation of recurrent event sequences; and language skills are needed to map words to observed temporal relationships.
In our view, the temporal updating system, with its sensitivity for ordered sequences, bootstraps the temporal reasoning system by furnishing the “and then, and then, and then” sequences where before-and-after relations can be noticed. Children's expanding event representations, along with developments in language and other cognitive competencies, provide the foundation for reasoning about temporal sequence. It is these developments that enable the shift from the temporal updating system to the temporal reasoning system.