10. Interpreting a graph
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| Task details | |
| Name of oral assessment task | Interpreting a graph |
| EAL curriculum level range | B1, B2, B3, C1, C2, C3 |
| Text orientation | Informative |
| Task type | Interaction and negotiation |
| Task specification | |
| Purpose | To assess students’ ability to explain their interpretations of what a graph shows. |
| Description | Students construct a graph as a group task, listen to a modelled explanation of what the graph shows, then we take part in a pair or group discussion of what the graph can show. |
| Assumed knowledge and description | Content knowledge: familiarity with collecting simple data and constructing a graph Text type, genre: verbal information report Linguistic structures and features: use of numbers and percentages; present tense: This graph / pie chart shows….; comparatives: X class is bigger than Y class; superlatives: X is the tallest student in the class, More students have, fewer students have; vocabulary related to the topic of the graph
|
| Learning/teaching context | |
| Language centre/mainstream class | Mainstream class – EAL Support |
| Subject/key syllabus objectives, outcomes | Mathematics |
| Topic/Teaching Unit | The graph construction can be linked to a class topic, such as favourite foods, travel to school, favourite TV shows, population of various countries, size of various countries, rainfall or temperature over a period of time. |
| Assessment conditions |
The kind of graph or chart used will depend on the age of the students, and on their familiarity with graphs and data. A simple pictograph or bar graph is suitable for younger students or those not familiar with graphs. Pie charts or line graphs can be used for older students. |
| Notes |
Pre-assessment activities can be extended or reduced as appropriate for the learners. Google ‘graphs for children’ for ideas. |
| Task implementation | |
| STAGE | ACTION STEPS |
| Pre-assessment activity |
If students have not had recent classroom experience with constructing and talking about graphs, they need to be involved in a simple activity to make their own graph, such as the following: Choose a topic for a graph, perhaps linked to a current classroom topic. In small groups students collect or research the data needed and then construct a graph. The teacher, using a similar kind of graph to those students have made, talks about what the graph shows, and doesn’t show. For example: ‘This is a graph of the size of all the countries where families of students in the class have come from. This graph shows the sizes of 10 countries. It shows that all the countries are bigger than 250 thousand square kilometres, but that none are bigger than 15 million square kilometres. It shows us that Vietnam is bigger than Sri Lanka. Some countries are too small to be placed on this kind of graph. It does not show the number of people in each country’. |
| Assessment activity |
Students in pairs or in groups of three discuss what their own graph is able to show, or not able to show. Younger students can discuss the graph with their teacher. Click to view the task sheet for this assessment: |
| Post-assessment activity | Students can ask and answer questions about their graph, with a partner. |
TEAL Oral Task 10- Unmarked criteria sheet [PDF]
TEAL Oral Task 10- Unmarked criteria sheet [Word]
An explanation of the purpose, nature and use of criteria sheets is available at 4. Using the assessment criteria.
Purpose and value of task
This task assesses students’ abilities to talk about the information they can read from a graph. Graphs are often used to accompany written texts and the basis of learning tasks in a variety of learning areas, so the capacity to understand and talk about graphs is an important foundation for learning across the curriculum. Mathematical language can be difficult for students of English because of the particular technical vocabulary only used in the context of maths, or common vocabulary used in precise ways in the maths context. For example, we often say, ‘wait a minute’, for an indeterminate amount of time, but in the mathematical context a minute lasts for a very precise amount of time. Grammatically, mathematical language can also be confusing, for example, the precise meaning of prepositions needs to be understood by students, and they may not perceive the difference between, count from 10 to …, count to 10, count by 10 to…
Students often have difficulty in extracting the mathematical problem from the ‘story’ around it, which can be very complex for EAL students to decode, for example, If I had 16 lollies and I wanted to give the same number to four of my friends, how many would they each get? Students who could easily solve the equation 16÷4= ? may not be able to extract this equation from a problem set out as a ‘story’. Talking about a graph has similar problems for students. This task is related to TEAL Writing Task 18: Information report based on a given survey.
Contextual information
The students in the samples were all prepared for this assessment task. The students in Samples 1 and 2 were involved in constructing the graph the day before they were filmed. The students in the other samples had all had recent classroom experience with graphs.
Commentary
All the students were able to talk about the basic information that their graph showed, answering basic and formulaic questions, often using the language the teachers used in their questions as they shaped their answers. Students at earlier proficiency levels were highly dependent on the familiarity of the context, and on the teacher using familiar and predictable language. The older and more proficient students were able to formulate more original replies, and were also involved in formulating questions about the graph they were working with, as well as answering questions they were asked. In some of the secondary samples the teacher asked questions that could not be answered from the graph. This not only assesses the students’ understanding of the graph, but also provides a check on the accuracy of the students’ listening skills in this context. He also deliberately gives wrong answers to questions the students ask him, making them give feedback and correction. It is also possible that students can answer questions about elements of the graph (reading headings and labels, talking about lines and boxes) without fully understanding what the graph is actually showing).
While the video samples cover the four levels of performance identified on the criteria sheet, the task could be performed more independently and with greater precision by students at higher stages than the target stages for this task.
Sample 1
Biographical information
Student A (left of screen)
Age: 12 years 11 months
Home language: Hazaragi
Student B (right of screen)
Age: 14 years 11 months
Home language: Hazaragi
Commentary
The students had constructed their graphs as a group activity the day before they were filmed, so the basic language and concepts were familiar to them. Both students are able to answer reasonably complex, but familiar, modelled questions about the graphs, such as, What were the most popular hobbies in Room 27? What was another popular hobby? However when other questions are asked, which are outside their immediate experience, they have difficulty. Both students at times seem to be guessing the answers, based on key words they are hearing. In particular when asked a ‘why’ question, students were not able to answer. The students are heavily scaffolded through the discussion, with the teacher pointing to the graph and using gestures, and rephrasing questions when necessary.
Student A
Student A was able to answer previously modelled questions about the graphs, but cannot really elaborate on his answers. When asked, What were the most popular hobbies in Room 27? he bases his answer on the teachers model, saying, The most popular hobbies in Room 27 is soccer. When asked if both girls and boys choose soccer, he answers, Just … most … boys. When asked why soccer was popular he is not really able to answer, saying, Because … soccer is … very good. He understands the idea of everyone having two votes, and is eventually able to work out how many votes there were all together. When asked the more complex question, Why did we choose to put our information, our data, about hobbies into this picture graph? his answer describes the process they went through rather than answering why they did it, Because … what you like and then you draw, and put. The teacher then asks, Is this easy for anyone to read? he agrees, but it is not really clear that he understands the question. He is then prompted to think about whether younger students would find a pictograph easy to understand, he answers, … take the ball, but again it is not really clear that he understands the meaning of the original question. When asked, How many more people liked drawing than volley ball? he immediately answers, Six (the number who like drawing), although he has just heard Student B answer a similar question correctly. Even when this kind of question is asked again, with gestures and at a slower pace, it is not clear that he has understood it.
The marked criteria sheet shows that the student meets some criteria at level 1 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level B1, Victorian Curriculum F-10 EAL.
TEAL Oral Task 10 – Criteria sheet – Sample 1 – Student A
Student B
When asked, What was another popular hobby in Room 27? Student B answers, Swimming pool. She knows how many students picked swimming and soccer. When asked again, What was another popular hobby in Room 27? she knows the answer, and tries reading ‘drawing’, but as she pronounces it, it sounds more like ‘driving’. She also knows which activities were not popular. She listens intently to the discussion of the teacher and Student A, and is then able to say why someone would recognise the drawing column, … one girl drawing. When asked how many more people liked soccer than swimming, she is able to answer, One more. She is also able to answer this question again in relation to other hobbies.
The marked criteria sheet shows that the student meets most criteria at level 1 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level B1, Victorian Curriculum F-10 EAL.
Sample 2
Biographical information
Student A (left of screen)
Age: 13 years 11 months
Home language: Dari
Student B (right of screen)
Age: 12 years 6 months
Home language: Hazaragi
Commentary
Both the students listen attentively to the teacher and to each other, maintaining natural eye contact with her and each other. The teacher moves away from simply asking a series of formulaic questions, and is instead able to conduct a discussion rather than a series of questions, which means the tone of the conversation is more relaxed.
Student A
Student A is generally confident in his answers, echoing the teacher’s first question in his answer, The most popular hobbies in Room 27 is soccer … all boys. He correctly responds to the question as to why the students mostly picked sports, saying, There’s a free time …. He understands the question about how many votes each student had, explaining, We do two hobbies, we pick two hobbies …, but seems confused when the teacher asks how many votes there were all together. He listens to the discussion about why they used pictures, and is able to comment, saying, Because it’s like a graph, and you can see a graph … and its pictures and names and …
The marked criteria sheet shows that the student meets most criteria at level 2 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level C1, Victorian Curriculum F-10 EAL.
TEAL Oral Task 10 – Criteria sheet – Sample 2 – Student A
Student B
Student B is fully engaged in the conversation, is quick to answer the questions, and clearly understands what the graph is showing. When asked if mostly girls or boys liked soccer, he confidently answers, most boys, (although he uses ‘mostly’ correctly later on when he says mostly girls, even though the teacher did not use the word in her question). He knows which the second most popular hobby was, and how many people chose it. He quickly understands the negative in the question, What wasn’t popular …?, even though it is not particularly marked in the teacher’s pronunciation, and correctly answers, ‘painting’. He understands the humour in the teacher’s comments about the students mostly picking sports, smiling and agreeing. He understands the generic term ‘sports’, and says about them, We have fun. He is quick to answer the question about why a picture graph was used to show the data, saying, It makes it a bit more clear, so you can see like a … how many pictures are in each activities. He agrees with the teachers following statements, nodding, saying ‘yes’ and clearly understanding what she is saying.
The marked criteria sheet shows that the student meets most criteria at level 2 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level B1, Victorian Curriculum F-10 EAL.
Sample 3
Biographical information
Year level: 6
Home language: Tetum
Commentary
The student listens carefully to the teacher, picking up on her verbal cues and gestures. He studies the bar graph, and then is asked what it is about. He answers, Telling you how much … how much blue are there … how much reds and what colours are there … When asked if it is telling how many colours or how many people, he answers, How many colours. After reading the title ‘Favourite Colours of My Class’ he says, How much people like the colours, showing that he understands the word ‘favourite’. He then seems to gain confidence, quickly answering the teachers next question, From this graph, which do you think is the favourite colour? He also quickly formulates his answer to the next question, Why do you think that? Saying, Because it has the highest number. He needs prompting to understand that the numbers represent people, but is then able to answer the question, What is the least favourite colour?
He again needs prompting to think further about the information the graph is showing, saying, Some people like pink and yellow, and some like red. He seems to have a good understanding of some mathematical language, responding correctly to questions such as, What is the second favourite colour?, Are there any colours that are equally liked? (Because it has the same amount of people likes the colour.) How many people do you think might be involved in this survey? How did you work out how many people were involved in this survey? (Adding the numbers up.) When the teacher queries his adding up, saying, I’m just a bit confused how you got the number 16 …, he adds the numbers again aloud, realises his error and corrects himself, saying, ‘20’. He can answer the complex question, If six people like the blue, how many people does that leave to like the other colours? He either does not understand or cannot yet work out a final question about percentages.
The marked criteria sheet shows that the student meets most criteria at level 2 of performance and some at level 3.
The student’s language use in this task is consistent with the descriptions of students at Level B2, Victorian Curriculum F-10 EAL.
Sample 4
Biographical information
Year level: 8
Home language: Persian
Commentary
The student gives a fairly confident description of what the graph is showing, cueing from the headings on the graph, It’s a graph about the rainfall … average in Australia 2013 … month, each month is how the rain falls … and show us how each one is the highest and which one is the lowest in this year … which month. He answers the questions about highest and lowest monthly rainfall totals, correcting himself when he makes an error.
He is less certain of the answer when asked, Which one had the highest average total? saying incorrectly, Is July again. When he is explicitly prompted to think about which line represents the highest average total, he gets the correct answer. However when the teacher asks him, When is that (the blue bars) below the average total? he clearly does not understand, and asks for the question to be repeated. The teacher explains again, saying, The monthly total is the blue column, when is that below the average, which is the black line. However, the student still gives an incorrect answer. The teacher asks if the blue column is above or below the black line. The student answers incorrectly, and it becomes apparent that he is confusing the meanings of ‘above’ and ‘below’. When the teacher, through further questioning and explaining, ensures the student understands these concepts, he is able to correctly name the months which are ‘underneath’ and ‘higher than’ the black line. The teacher uses ‘underneath’ instead of ‘below’, and ‘higher than’ rather than ‘above’ for these questions.
When requested to ask the teacher two questions about the graph, the student is at first reluctant, but eventually asks, Why … er …May and June have the black line under blue, but July didn’t, it’s like …, showing continuing confusion about the meaning of words for spatial relations. For his second question the teacher prompts the student to ask about the amount of rainfall, but the student is not able to do this until the teacher demonstrates a question and answer. The student is then able to ask, How, like August … have average total … in black line … The teacher’s answer demonstrates a more formal construction when he answers, The average total for August would have been, maybe 25 …, and the student agrees, saying, Maybe … His third question, Is that there … March and January the same average, have the same average total. The teacher deliberately answers incorrectly, saying, I think January’s is about 100 ml higher. The student says that the teachers answer is correct, and only through unpacking the problem does he see that the answer is incorrect.
This video shows that even though the student seems to understand what the graph is showing, incorrect or incomplete knowledge of the words for quite basic concepts leads to confusion and misunderstanding. The student’s ability to ask questions framed in mathematical language is more limited than his ability to understand them.
The marked criteria sheet shows that the student meets some criteria at level 2 of performance and some at level 3.
The student’s language use in this task is consistent with the descriptions of students at Level C1, Victorian Curriculum F-10 EAL.
Sample 5
Biographical information
Year level: 8
Home language: Persian
Commentary
The student gives a reasonably confident explanation of what the graph shows, cueing from the headings, Is Australia rainfall for 2013 by month, blue part is a monthly total. The black part is average total from 1961 and 1990. He adds in his own words, I think it’s all the rainfalls, and January I think got the highest rainfall, August got the lowest rainfall.
He doesn’t fall for the teachers trick question, answering, It doesn’t say. This student also has difficulties with the questions about the highest and lowest average totals. When asked, Which month was below the average total? he correctly answers January, but is then not able to name any other months. It is not clear why he has difficulty with this question, and even after the teacher deconstructs the problem and finally asks, … so which blue ones are below the black ones? he is still not able to answer. He eventually tentatively answers ‘December’, but it is clear he still does not really understand the question. When the teacher changes the question to which months are below the average he is able to tentatively get the correct answers. He may, like the student in Sample 4, not really understand the meanings of ‘above’ and ‘below’, in this context, or it may be the form of the questions which confuses him.
When he asks the teacher questions, his grammatical features are more advanced than the student in Sample 4. He asks, What’s the average total of September? and What’s the highest average total?
The marked criteria sheet shows that the student meets most criteria at level 3 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level C2, Victorian Curriculum F-10 EAL.
Sample 6
Biographical information
Year level: 8
Home language: Karen
Commentary
The student gives a good initial explanation of what the graph shows, with less reliance on the headings on the graph itself, than the students in Samples 4 and 5. He says, This is, like, the graph about Australian rainfall for 2013, it goes up by 20 (ml), on the bottom is the month of the graph, the black line is the average total, and the blue one is the monthly total. He is able to answer questions about which months are above and below the average totals, which confused the students in Samples 4 and 5. He also is not misled by the trick question, saying, It’s not on there. He can correct himself when he makes an error, after the teacher repeats the question.
When it is his turn to ask questions, he playfully asks the teacher, What’s the total average for all of them? He follows up by asking, What’s the highest? and knows when the teacher provides an incorrect answer. When the teachers asks, The highest average or the highest month? he answers, Both, and again knows when the teacher makes an error.
His conversation with the teacher is more relaxed and fluent than the previous students, which is related to his higher level of English language proficiency.
The marked criteria sheet shows that the student meets some criteria at level 3 of performance and some at level 4.
The student’s language use in this task is consistent with the descriptions of students at Level C2, Victorian Curriculum F-10 EAL.
Sample 7
Biographical information
Student A (left of screen)
Year level: 8
Home language: Italian
Commentary
The students conduct a quite formal discussion, based on a series of questions and answers, with Student A asking most of the questions. Only Student A provides enough language for a commentary and analysis.
Student A (left of screen)
Although a series of questions are written on the graph itself, Student A does not rely on these when asking his own questions. Although no other immediate language models are available during the interview, he devises a carefully thought out series of questions for Student B to answer, using a range of question types, for example:
- What does this graph show?
- And now what’s the … what’s the first name …
- And now … so we are getting better, like … longer life … and … um … can you just say to me what are the factors, ah, do you think … why are we getting better and better?
- How long would people expected to live in Classic Rome time, like? And what about the Classic Greece?
- And … how many … Britain time?
- …and lets go a bit, long time ago (?) in Bronze Age?
His range of question types is quite broad, and he varies his questions even when asking for the same type of information, as in questions 4, 5, and 6.
He also makes an observation, which could be construed as a question, Can you see how the graph is like … the line of the graph is getting like … there was a life expectancy … less than … now is very good, the life …, to which Student B replies, Yeah, so … it goes like down and up and down …
He provides a final summing up statement at the end of the interview, saying, So this time is the worst one that we live in, yeah, and the best one is now.
The marked criteria sheet shows that the student meets some criteria at level 4 of performance.
The student’s language use in this task is consistent with the descriptions of students at Level C3, Victorian Curriculum F-10 EAL.
Using the assessment to improve learning
Comparative language can be challenging for students, but is used in many contexts. Students can familiarise themselves with the patterns around making comparisons with a substitution table to make sentences (true or false) for other students to answer, such as:
| More | students | like | soccer | than | soccer |
| Fewer | people | don’t like | drawing | drawing | |
| The same number of | swimming | swimming |
Students can fill the gaps in tables such as:
| big | bigger | |
| small | smallest | |
| taller | ||
| older | ||
| youngest | ||
| happier | ||
| sad |
Older students can practise writing questions and answers, based on sentence starters:
What does the … show?
The graph shows the…
The blue line depicts…
The highest…
The lowest…
The rainfall for August is…
