(2016) Misconceptions, Teaching and Time

Wood-Wallace, D (2016) ‘Misconceptions, Teaching and Time’ The University of Nottingham (PGCE): Academia

Misconceptions, Teaching and Time:

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1 — Rationale

The focus for my school based inquiry was to examine the most common

misconceptions that are held by pupils when learning about Time and to explore how

teachers seek to address them in their teaching (see appendix 1e for sub questions).

The research thread emerged from the alliance topic ‘to investigate ways to develop

deep conceptual understanding and handle misconceptions within a particular

mathematical topic’. It was anticipated that Time would be a suitable mathematical

realm to research due to the variety of misconceptions that are commonly attached to

the objective (LittleStreams, 2015). Time appears as a statutory objective in the

Primary National Curriculum under the mathematical program of study of measure

(DoE, 2013), it is evident in every year group with increasing degree of complexity

until year 6 (appendix 1a); by which point pupils are expected to know and be able to

use all skills relating to the concept. The present description is based on a 34

interview corpus of data carried out in an inner city Nottingham school,

Nottinghamshire, United Kingdom between December 2015 and March 2016. The

informants included in the study represent teachers, Newly Qualified Teachers (NQTs)

and Teaching Assistants (TAs). The data collected comprise of 22 questionnaires and

12 interviews. The motive for this arrangement will become clear when the

methodology is discussed. The analysis was undertaken in order to understand what

teachers consider to be the key issues embedded within the teaching of Time, what

the observed most common misconceptions are; and how teacher’s perceptions of

these and practices in response to these can implicate on future teaching.

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2 — Literature Review

Within recent years the terms ‘misconception’ and ‘conceptual understanding’

have been somewhat buzzwords within the education field, especially since the

introduction of the ‘mastery’ element within the new National Curriculum (DoE, 2013;

NCETM, 2014). Examining the literature ‘mistakes’ and ‘misconceptions’ are

occasionally used interchangeably; however it is worth highlighting the difference

between the two. Mistakes, as defined by NCETM, can be made ‘through errors,

through lapses in concentration, hasty reasoning, memory overload or failing to notice

important features of a problem’ (NCETM, 2009). These are generally ‘one-offs’ that

do not consequently hinder a student’s progress in the learning of a new concept.

Differing from this, an error can sometimes be made as the result of a misconception

or partial conception that a learner has in connection with a concept. The

constructivist view would argue that this is due to learners attempting to construct

meaning with the new knowledge, and as a consequence will sometimes over-

generalise or link to existing experiences that they have in order to try and make

sense of it (Cobb et al, 1992; Pinker, 2003). Errors of this type will be consistent and

due to an alternative interpretation that a learner has formed on a mathematical idea,

which can hinder and act as a barrier against a learner’s progress in acquiring new

knowledge. Employing this distinction the following analysis focuses solely on the

misconceptions that pupils commonly form, not the mistakes that they may make,

during the process of learning the concept of Time.

2.1 — Misconceptions

It is generally agreed within the literature that misconceptions are

unpreventable (Swan, 2001) and, if unchallenged, can affect the learning and

acquisition of new concepts (Engelmann and Huntoon, 2011; Kambouri, 2012). In the

past there was a strong consensus of seeing misconceptions negatively as ‘barriers to

understanding’ (Moore et al, 1997: 27), however, more recently numerous research

enquiries have evaluated the positive impact that dismantling misconceptions within

the lesson can have on achieving a deeper level of conceptual understanding (Boaler,

2014, 2015a,b; Dweck, 2006; Moser et al, 2011). Evaluating the literature, it seems

that the dispute now lies in the timing of when misconceptions should be introduced

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and addressed, and whether or not it should be the teacher (Curwin, 2014; Young,

2012) or the pupil (Askew and Wiliam, 1995; Swan, 2005) who initiate the teaching

around a misconception.

Young (2012) defends the use of misconceptions as a teaching tool and argues

that actively supplying pupils with misconceptions to unpick, such as ‘spot the error’

or ‘odd one out’ (Drury, 2015); is a productive way to deepen their understanding of a

topic. This approach seems valid as pupils are able to identify their own and others’

errors and, through discussion and reflection, understand and correct the

misconceptions that underlie them. A similar outlook is shared by Curwin (2014) who

articulates ‘it’s a mistake not to use mistakes as part of the learning process’ (Curwin,

2014: 1). Curwin argues that teachers can find value in error and should teach

through misconceptions to allow and promote deeper learning. The theory behind this

strategy is that the risk of pupils then going on to make those mistakes within their

work will consequently be reduced (Longfield, 2015). This position sees

misconceptions as a strong part of the learning process, they are embedded within

the lesson so pupils not only learn why a procedure is right, but are also able to

identify and reason why a method is wrong. However, critically analysing this method

also reveals some potential issues. For example, the approach fails to consider the

wide and varied nature of misconceptions, which can make the selection of

misconceptions for a planned teaching approach extremely difficult and arguably,

futile (Sadler et al, 2013). Equally, teaching misconceptions before pupils have made

them relies heavily on presumption, and so it could be argued that teaching

misconceptions that pupils were possibly never going to make is a waste of valuable

teaching time (Smith et al, 1993).

Juxtaposing actively setting out to teach misconceptions as part of topic

content, Askew and Wiliam (1995) advocate that it is more effective to address

misconceptions when and if they arise, insisting that drawing attention to

misconceptions before pupils have made them is ‘less effective than letting pupils fall

into the ‘trap’ and then having the discussion’ (Askew and Wiliam, 1995: 13). What

Askew and Wiliam mean by this is that a deeper level of learning is retained when it is

pupil lead rather than teacher initiated. Similarly, Piaget also hypothesises that we

learn better when we discover ourselves, and that a discovery model enables learners

to own beliefs and concepts in a way that transmission models (which misconceptions

as a teaching tool arguably falls under) do not (Piaget, 1964). Agreeing with this,

Swan (2005) contends that planning to teach a misconception prevents the organic

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cognitive conflict that a learner would usually go through when recognising

inconsistencies between what they already know and what they are being told, and as

such will not be able to formulate a deep conceptual understanding around the error

because they would not have conceived the misconception themselves. Teaching

misconceptions at the point of identification claims to improve long-term retention of

knowledge (Anghileri, 2006) however; critically evaluating it also foregrounds some

potential issues. For example, it fails to utter how the approach accounts for

misconceptions that do not surface within the lesson (Gammon, 2004), and refuses to

take responsibility for how this can impede on future learning (Yates and Marek,

2014).

2.2 — Time

The present study focused specifically on the teaching of Time due to the

variety of misconceptions that it frequently presents (McMillen, 2008). Surveying the

literature it seems that Time is, and always has been, a difficult concept for teachers

to teach and for children to understand (Monroe et al, 2002; Piaget, 1969). McGuire

(2007) argues that this is because Time does not easily link with other topics of

measurement, or even with the wider objectives within mathematics. For example,

Time relies on multiple uses for the digits on a clock face (Mathematics Navigator,

2015) and a base of 60 instead of 100 in place value algorithms (Ojose, 2015). It is

thought that these concepts conflict with alternative concepts pupils are concurrently

forming, such as place value having a base of 100, and so many misconceptions can

form (Thanheiser, 2009).

Although there is extensive research documenting the difficulties with teaching

Time; there seems to be little, if any, literature covering how misconceptions in Time

are dealt with. Harris (2008) focused on the types of misconceptions that commonly

form, such as difficulty in understanding points in Time, Time intervals and Time span

(PMPT, 1981), however failed to deduce when the optimum time to correct them

would be. Equally, Grauberg (1997) theorises that misconceptions can form because

pupils need to grasp two different aspect of Time simultaneously: the concept of Time

and how to tell the Time, but also did not consider how and when these

misconceptions should be addressed. The present study aims to address this lack of

research by examining how and when misconceptions in Time are dealt with in the

classroom.

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3 — Methodology

The methodological design behind the present study was based on an

amalgamation of both quantitative and qualitative research. Quantitative research

claims to be as objective as possible as it is mainly based on empirical data and

statistics (Neuman, 2005). Using this approach suited the study as it allowed

perceptions to be clearly measured and analysed, thus giving a numerical value of

preferred approaches (Minichiello, 1990). Differing from this, qualitative research

relies on a more subjective approach, allowing the researcher to delve into informant’s

attitudes and opinions to draw a conclusion (McLeod, 2008). Though no statistical

generalisations can be made from using this approach (Cresswell, 2009), it was

envisioned that the data collected via this method could help to explain the

perceptions that were collected quantitatively.

3.1 — Variables and Selection of Participants

In order to keep the study representative of teacher’s perceptions, the only

controlled variable was that participants had to be involved directly with teaching

pupils the concept of Time. From this, participants were stratified based on job role

into three categories: teachers, newly qualified teachers (NQTs) and teaching

assistants (TAs). This was incase any patterns could be drawn in light of these

classifications. Another experimental variable was the level candidates taught, again

due to the potential of patterns emerging from these categories. In order to make the

study fair, as long as participants fitted the controlled variable above they were

permitted to partake in the study. This meant that a random sample of each of the

experimental variables were collected.

3.2 — Ethics

To ensure the research remained ethical, a number of steps were taken to

safeguard participants and data. Adhering to the ethical guidelines for educational

research (BERA, 2011), all participants signed a consent form which clarified the

purpose of data collection and their right to withdraw, and informed them how their

data would be used confidentially (appendix 1b).

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3.3 — Method

To test that the data collection methods were viable a pilot study amongst

family and friends was circulated (Teijlingen and Hundley, 2001), and once there was

confirmation that the techniques were effective the main study began. Questionnaires

(appendix 1c) were distributed within the school internal mail to the three groups

specified above as a way of collecting quantitative data. Responses were optional and

anonymous (though it was asked that participants filled in the variables section of the

form). 22 questionnaires were returned. Interviews (appendix 1d) were carried out

with staff on a voluntary basis if they wanted to voice feedback outside of the

constraints of the questionnaire structure, and hence contribute qualitative data. In

total, 12 interviews were conducted.

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4 — Results

The results will be presented in a number of ways in order to evaluate the main

misconceptions pupils have when learning about Time and how teachers seek to

address them within their teaching. The raw data gathered via the questionnaires will

be grouped under the four sub questions set out in Appendix 1e (and hence, arranged

in four tables). As the study specified two experimental variables (see section 3.1),

the findings from these will also be included. For each question in the table there will

be an overall response score (top row), then a breakdown of this percentage by job

role (middle row) and age-range candidates teach (bottom row). This is to expose any

patterns that may transpire in relation to the experimental variables. Finally, the

results gathered via the interview method of data collection will be discussed if the

responses contribute to the findings in the questionnaire.

Responses to the questionnaire were optional and anonymous (see section 3.3),

and as such a random sample of each variable were collected. In total 22

questionnaires were completed. 16 responses were from teachers, 1 from a newly

qualified teacher and 5 from teaching assistants. In terms of age-range participants

taught, 6 were completed by participants in key stage 1, 7 by lower key stage 2; and

9 by upper key stage 2. When completing the questionnaires, respondents sometimes

marked more than one answer or left a question completely blank, and so the results

tend to be loosely constricted. Due to this, and the mixed sample of questionnaires

returned, the present study makes no general claims from the findings observed; and

instead aims to probe some potential conclusions to warrant further research.

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Due to the overarching aim of the essay to examine how misconceptions are

addressed within lessons, it was thought that question 5 should be examined in more

detail.

Fig 6. Question 5 - How do you address misconceptions within your own lessons?

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5 — Discussion

Analysing the results in their entirety (Fig1-5) generally show an even spread of

responses between the set variables outlined in the questionnaire (appendix 1c).

However, when the findings are scrutinised closely, it is evident that there is great

variation between the responses collected within the two experimental variables

(specifically within Figs2,4).

Results and discussion in response to the sub questions outlined in appendix

1e:

• Teachers generally find Time a fairly easy objective to plan, resource and teach

(Fig1,3). This seems to contradict previous research (Monroe et al, 2002; Piaget,

1969), which argue that teachers find Time one of the most difficult concepts to

teach

• The aspects of teaching Time that teachers feel present the most misconceptions

shift between the age-ranges taught (Fig4). However this was expected as aspects

of Time that pupils struggle with will no doubt alter as the complexity within the

statutory yearly objectives increase (appendix 1a)

• The misconceptions identified as ‘common’ (Fig4) are in line with those Graugberg

(1997) and Harrison (2008) report. Interesting, the misconceptions specified

within Fig4 were also submitted as ‘most-common misconceptions’ during the

interview process (appendix 1d), even though candidates did not have the

questionnaire (appendix 1c) to draw answers from

• Teachers feel that the best time to teach/correct a misconception in relation to

Time are when they arise or the next day. This supports research conducted by

Askew and William (1995) and Swan (2005)

• 85% of teachers feel that unpicking misconceptions gives pupils a deeper level of

understanding in relation to Time. This supports existing literature (Boaler, 2014;

Dweck, 2006, Moser et al, 2011)

One of the most interesting results emerged from responses to question 5 (figs

2 and 6). When asked how misconceptions are addressed within respondents’ own

lessons there seemed to be an even split between teaching ‘when they arise’ (42%)

and ‘the next day after marking’ (38.7%), supporting research carried out by Askew

and Wiliam (1995) and Swan (2005). Only 16.1% planned to use misconceptions as a

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teaching tool, as suggested by Young (2012) and Curwin (2014). Analysing this

further (Fig6), we can see that all of that 16.1% is contributed by teachers of upper

key stage 2. Though no conclusions can be drawn as to why only UKS2 teachers plan

to teach misconceptions as part of topic content, the interviews conducted with

respondents (appendix 1d) did offer some reasoning. Responses included ‘not

knowing common misconceptions well enough’ to plan a teaching activity and being

‘unaware of the variety of misconceptions’ pupils can have. Perhaps most interesting,

was the response ‘teaching misconceptions tends to confuse pupils more as you are in

effect telling them to learn something new that is wrong’. This response seems to

juxtapose all research that advocate misconceptions as a tool for achieving deeper

conceptual understanding and instead retreats back to seeing misconceptions as a

negative step in pupil learning. Whatever to reason, there seems to be a distinct lack

in misconceptions being used as part of topic content during the learning process.

5.1 — Implications of findings for the school

The present study concludes 3 implications from the findings of the inquiry for

the school to consider:

• Fig 2 and 6 show the variety of ways misconceptions are dealt with in the lesson -

It is suggested that the school look into the lack of whole school approach for

dealing with misconceptions

• Feedback from the interviews carried out revealed teachers are ‘unaware’ and ‘do

not know misconceptions well enough’ - It is suggested that the school look into

offering CPD around subject knowledge

• Fig 5 shows that 85% of teachers agree that unpicking misconceptions gives pupils

a deeper level of conceptual understanding - It is suggested that the school look

into teaching misconceptions as part of topic content through tasks such as ‘spot

the mistake’ and ‘odd one out’

5.2 — Implications of findings on future practice

In light of the implications for the school identified above (sections 5.1), I have

identified 3 implications to consider for my future practice as a teacher:

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• Having an awareness of the common misconceptions associated within Time and

how to plan these into lessons to effectively for pupils to unpick should enable a

deeper level of conceptual understanding to be reached

• Subject knowledge plays an important part of teaching pupils concepts such as

Time - I need to be ensure there is both breadth and depth within my subject

knowledge, and that this is updated regularly

• Figs 1 and 3 evidenced the usefulness of resources when planning to teach pupils

concepts such as Time - I need to ensure that I research the wide range of

resources that can accompany the teaching of Time, and ensure that I look into

the pedagogies of how it can be taught effectively

6 — Conclusion

To conclude, the focus for my school based inquiry was to examine the most

common misconceptions that are held by pupils when learning about Time and to

explore how teachers seek to address them in their teaching. The research found that

overall there was no agreement between the most common misconceptions pupils

develop (Fig4), and that this could be because the most common misconceptions

pupils’ develop shift between that age-ranges taught. In spite of this, the research did

confirm that the misconceptions identified as ‘common’ were in line with those

specified by Grauberg (1997) and Harrison (2008).

In analysing how teachers address misconceptions within their teaching, it was

observed that in line with the works of Askew and William (1995) and Swan (2005),

most teachers generally teach/correct a misconception when it arises or the next day

after work has been marked. However, it was noted that the low findings for planning

to teach a misconception as part of lesson content could be due to teachers’ own lack

of subject knowledge, and absence in knowledge of the common misconceptions

pupils may have and where these would appear within the different key stages. The

study also highlighted some implications of findings for the school to consider, and for

myself to consider within my future practice as a teacher.

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Documents

(2016) Misconceptions, Teaching and Time