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Interactive Teaching in the Classroom
Ideas for discussion based on
Interactive Maths Teaching by Nick Pratt (Paul Chapman: 2006)
Dr Angela M. Horton, University of Exeter, UK
Creating a Learning Community in the Classroom
Learning is not just about acquiring a body of prescribed knowledge. Rather it should be an attempt by learners to explore the ideas that make up the subject (for example, Maths, Language, History, etc.) – and come to know them through that exploration. The focus should be on the process of exploration with the “coming-to-know” as its by-product, not the other way round.
Learning about a subject involves:
- DOING it: engaging in activities that develop processes and procedures and a sense of the subject;
- USING it: seeing the potential of the subject in the real world and within itself and making use of it in relevant ways;
- KNOWING the subject: developing knowledge and understanding.
Developing Lesson Objectives – a wider view of “understanding”
How we teach directly affects not just children’s attitudes, but also the form of knowledge that they develop. Children who learn in a climate of enquiry and who engage in problem solving regularly tend to develop knowledge that is more flexible and can be put to use more readily. “Understanding” is not something that happens at a given moment in time. It is not absolute or permanent. Many of us have been led to believe that understanding is acquired in varying amounts and that it is easy to measure this in individuals. Is this really true? Alternatively, we can view “understanding” as having many facets (one aspect of understanding connects to many others) and these elements can constantly be developed. Does this view help to explain why “understanding” is difficult to measure? Schooling is often organised around principles which imply that understanding is fixed at any one moment. (How often do we read curriculum statements that say, “ Learners should be taught X?”) Objectives set in this way can be seen as end points. Alternatively, if understanding is seen as something complex, which can continuously develop but is never complete (since an idea in any subject discipline can be linked to other ideas or understood in new ways), then we need to create a context and use strategies that allow children to become more aware of what they already understand and then help them to construct further understanding. Lesson objectives can be developed as centre-points around which an exploration may take place, rather than as end-points.
Having a flexible view of “understanding” means that, after the learning experience, assessing “how understanding has changed” is very different from assessing “what has been understood” – which is what is more frequently done in classrooms. The latter is more likely to lead to labelling (success or failure to understand) with the focus on the superficial aspects of the learning. The former leads to a more sophisticated, student-centred assessment of how the student is developing his/her thinking. Of course, the learner feels much safer when talking about “developing or improving his/her understanding” rather than simply noting whether “understanding” has been achieved or not. The former clearly implies that progress may be slow, that it is OK not to understand at the start, that everyone will have different levels of understanding and so on. The latter simply puts learners into the “able” or “unable” group, which rarely leads to effective, more complex learning for anyone. As part of ongoing personal development, every act of understanding is, to varying degrees, related to our culture (what we know and what we consider normal, everyday), our history (what we have experienced before and what sense we have made of it) and our social setting (the context within which we are understanding as well as our relationships with the teacher and other students there).
Structuring interactive discourse that does not close down the exploration of ideas but seeks to keep students exploring, so that they can construct complex “understandings” PRACTICAL EXAMPLE 1
In the following example, the teacher interacts with a class of Year 3 students who are trying to calculate 7 X 13 as part of a larger problem they are tackling together.
How does the teacher manage the class in order to keep the emphasis on mathematical thinking and also ascertain what is accurate?
Teacher: So, let’s gather together some of our responses.
Amy: 80 (inaccurate)
Teacher: (writes 80 on the board without giving away the inaccuracy of the answer.) Anyone get a
different answer?
Taro: 91 (accurate)
Teacher: (again writes 91, not revealing the accuracy). Any more answers?
Gita: 90 (records 90 on the board, as before)
Teacher: OK, we’ve got 80, 91 and 90. Who can argue for their answer?
Amy: I can. Seven 10s are 70 and 7 add 3 is…..
Luke: (interrupting) No. It’s not 7 add 3, it’s seven 3s which make 21.
Teacher: Amy, can you argue back? What do you think?
Amy: (thinks)….. No….. it’s 91
Teacher: Gita, what do you think?
Gita: Luke has made me think and see it differently. I think it’s 91 now.
Teacher: OK, 91. Looks like we all agree. What other mistakes might we make when trying to do 7 x 13?
Noel: We might say 7 add 13 and make 20.
The conversation continues briefly to look at this,
In this example, the teacher facilitates discussion between pupils, listens carefully to their responses and encourages the students to be the judge of whether or not something is accurate. The teacher makes no comment about what is right or wrong but, rather, helps the students to think about that.
The teacher focuses on completeness: finding ALL the examples of something, rather than just one example. However, there is also a vagueness in the task, leaving room for students to interpret the problem in different ways.
PRACTICAL EXAMPLE 2
Compare the dialogue between teacher and students in Practical Example 1 above with the following example.
The teacher is working on the properties of two dimensional shape with his Year 4 group who all have a set of plastic shapes on the table in front of them. The following dialogue takes place:
Teacher: Hold up a regular pentagon. How many lines of symmetry does it have?
Jane: One.
Teacher: One. Why do you think that?
Jane: Because the only way you can fold it is straight down the middle. (The student indicates a line vertically down the centre.)
Teacher: What do other people think?
Tom: Five. (the accurate answer)
Teacher: Five. That’s right. Well done. Now, everyone, hold up regular hexagons. How many lines of symmetry to they have? Remember?
Whole class: Five!
_______
Note how the teacher’s first question, and the task (to find the regular pentagon) imply that the children are about to be involved in a discussion about the properties of shape. But in fact, this is not what happens. By asking for other children’s ideas when the inaccurate answer is given, but moving on immediately when the accurate answer is given, the teacher’s intention behind his actions seems more to do with hearing accurate responses.
How might this have felt different if the teacher had asked again what other people thought in response to Tom without revealing whether five was right or wrong?
In which of the Practical Examples above did the students learn most?
What would have happened if the teacher had said:
- “Interesting. What do other people think of that?”
- “Can you tell us more about how you came to that answer?”
- “Can anyone think of a reason why Tom’s response is different from Jane’s response?”
When talking to learners, teachers often require “the” answer. For example, a kindergarten teacher may start a lesson by saying, “Who can tell me what a triangle is? A student may give a response that the teacher wants, representing a facet of what a triangle is. The other students are expected to remember it. There is no further investigation. Alternatively, the teacher could say, “ Who can tell me something about triangles? Anything is fine.” Several students can then articulate what they know, gradually building up a more sophisticated representation of what they understand about triangles. They can go on to have experiences in the classroom and keep exploring ideas about triangles that will help them to construct together some new, deeper understandings.
We all know that a foreign language can either be taught and then used (that is, the teacher can cover a set of ideas and then ask the students to use them). Or it can be taught through its use. Being taught a foreign language through its use implies the need for communication as the motivational driving force behind the development of the language. Similarly, the need to communicate about a subject discipline within a classroom can similarly drive the process of making sense (making meaning). From this perspective, communication leads to uncovering ideas (for example, mathematical ideas, historical ideas, scientific ideas) and constructing meanings. Therefore, we need to create classroom tasks in which communication about the subject discipline is an integral part of the task, a highly valued part of the work, not incidental to it.
Therefore, we need to set up a discourse with students. This has three elements: a) what is said; b) what is done; c) what is expected of students. We need to create tasks for students to talk about that help them to diverge towards many different, interrelated ideas and understandings, NOT converge on one answer that the teacher expects. It is very easy when under pressure, managing a class of students, to revert to what is right and what is wrong. In particular, if our focus is on objectives as the end points of lessons, we can easily drive students towards particular information rather than allowing them to use language to develop fuller understandings together.
Responding to students The way teachers react to student responses is important.
In your classroom, which of the following things can you catch yourself doing? Ask yourself, why are you doing each one and how is it useful, or not, in your teaching?
- you interrupt student answers to questions and/or finish them off in your own words.
- You re-interpret what a student has said to mean something different.
- You ignore a student’s whole answer because it did not match your teaching point.
- You ignore a student’s whole answer for fear that other students could not understand it.
- You ignore parts of a student’s answer in order to re-focus it on something new that suits your purpose better.
- You repeat the student’s answer, but emphasise certain parts of it to change the meaning.
- You choose which student answers to respond and deliberately ignore unwanted responses that do not suit your teaching point.
- You say, “Good”, “Well done” or “I’m not sure about that” to give value to certain student answers instead of letting students decide about the accuracy or the appropriateness of a response.
Of course, doing these things is necessary and quite appropriate much of the time. After all, we cannot just let the classroom discussion meander aimlessly wherever it wants to go. Focusing students on particular points is often an effective way to support their thinking too. However,
if it becomes habitual and constant, students soon learn that you are not genuinely interested in their responses and in the inquiry you have set them except in so far as they serve your teaching purpose. Students then return to the game of providing the teacher with the answers she or he seems to want.
Teachers’ interactions with students involve a balance between the ongoing talk and management of the lesson relating to the subject discipline and the background classroom management. The most effective interaction is likely to happen when students focus explicitly on the talk and tasks of the lesson (that is, the subject discipline) - tasks that have a real purpose and meaning for them – with the classroom management being implicit in the background.
Sometimes students complain that they can’t hear or follow what other students say. Therefore, if what a student is explaining seems to be useful, it is important to encourage students to position themselves and to speak in such a way as the whole class can hear. It is also important to encourage students to keep clarifying what they have to say until everyone understands.
Counterbalancing this, the teacher also has the difficult task of trying to ensure that a sense of debate is kept alive in the lesson by keeping the inquiry focused on different aspects of the work that drive the inquiry forward. (“What is another way of looking at this?” “Are there other explanations.” What might make you think that student X’s response is appropriate?” “Have you seen other examples of this elsewhere and do they help us understand better what we are thinking about here today.”, “Is this true for all people in the world?”) If a student is explaining something that a lot of other children in the class already know, this becomes boring for them. Asking students to justify their point of view (“What makes you say that?” “Can you convince us that what you say is accurate?”) is valuable for drawing out the essential elements of a concept, a process, etc. Similarly, asking other students to justify someone’s response can keep everyone focused on searching for the underpinning rationales. (Who can think of a reason why student X’s response might be accurate?)
Designing classroom tasks that make children want to inquire and talk
A good classroom task has a creative ‘purpose’ for students and also the students will have an ‘audience’ to present their work to. (Often this will be other students in the class, but it could also be students in another class, a visitor, another teacher, etc.) It is important for students to have a definite product to create (mental or physical) –a goal to achieve. If the students are asked after a lesson what they did in History today, they need to be able to say, “We created a poster.”, “We wrote a newspaper article.”, “We drew up a list of criteria for examining artefacts.”, “We made up a quiz to find out what people know about the complexities of examining historical documents.”, “We designed a page for a text book we are creating for next year’s Grade 8 history class about how to compare two, conflicting eye witness accounts of a particular event.”, “We worked in pairs to evaluate a history essay written by a student in a previous year, in order to identify its strengths and weaknesses in relation to the “criteria for successful work” that the teacher and students had identified together at the outset).”, “We prepared arguments for both sides of an issue, ready for a debate about X.” “We planned a display to show people’s different interpretations of historical evidence …..” “We created a plan for exploring our local history…. (or finding out more about X).”
In order to plan creative tasks like these but also to keep students focused on elements of the curriculum that they are required to address, it is helpful to:
1) Plan tasks that are set in the context of an inquiry.
2) Create a need to communicate.
3) Require outcomes of learning to be recorded in different ways (oral presentation, written prose, poster, list, “TV/radio show”, newspaper article, poem, exhibition, science day, short drama scenes or a play, piece of art work with accompanying text, model, sketch, diagram/drawing, physical PE display.
Simply turning all your lesson objectives around into questions and trying to find something problematic to think about, will immediately make your lessons inquiry-based. For example:
National Curriculum requirement Curriculum requirement turned into an
inquiry
Know all multiplication facts up to 12 x 12 Which multiplication facts are the
Difficult ones and why? What advice can you
offer for learning them?
Understand the parts of a plant. Do all plants have the same parts? What might
be the reasons for the parts all being the same
or different?
Learn about the place holding function What do zeros do in different numbers? How of zeros. could you explain this to someone who doesn’t
know?
Learn about the countries conquered by Is the evidence that Chingis Khan and his by Chingis Khan and his descendants. descendants conquered many peoples clear
and incontestable?”
Learn about past participles in English. Are past participles in English all the same?
Can you find an interesting way to show
what rules govern the way they are constructed?
Learn about how the human eye works. Investigate whether human beings all see in the
same way? Make an oral presentation, supported
by diagrams with captions to show the outcomes
of your investigation.
Learn how to do different kinds of jumps Which are the most difficult jumps to do and
in Physical Education. Why? Can we make an oral/written list of
instructions to show people how to do them
successfully? Can we test our instructions out on
other students and refine them if necessary?
Learn about division using decimals. Can we find as many ways as possible to
illustrate how to divide using decimals
to help someone who does not understand this?
Managing the inquiry
a) Split a task up into sub-tasks that need to be brought together again for a full picture to emerge.
b) Provide a choice for students in terms of the questions they tackle in a task, so that they don’t all do the same ones.
c) Split the class in two, asking each half to investigate a similar but different topic over two (or more lessons). Towards the end of each lesson, ask students in one group to provide advice to the other group about how best to continue the work in the next lesson.
d) During the main part of the lesson, identify students who have found novel approaches to the task, or something else worth seeing and ask them to give a short explanation/demonstration in the last 10-15 minutes of the lesson.
e) Ten minutes before finishing the lesson, ask students to choose ‘something special that others probably won’t know about’ and to talk to the whole class.
f) Encourage students not just to tell others about their ideas, but to set the class ‘test questions’ to see if they have understood it together and can use it themselves.
g) Instead of providing worksheets with, say, 10 mathematical problems to work out, provide just the first 3 and then ask students to create some more for other students – and work out what the answers would be.
h) Ask students to choose just 3 or 4 questions from a sheet of 10 and complete them. Then get them to annotate their responses to show what they were thinking about as they did them and how they were done. Ask students to share their annotations/thinking with each other.
i) Challenge students to create their own textbook pages for another student. The page should include sections explaining the ideas involved and then some questions that test the other student’s understanding. Think about how questions may be graded to get progressively harder.
j) Present students with worksheets that you have completed yourself, deliberately getting
some questions wrong. Ask them to mark the work as if it was done by another student and
to think of constructive feedback to give to them. By making some of the errors systematic,
you can model common misconceptions and errors.
k) Have a “Top Tips” (Advice) notice board on the classroom wall where students can post
advice to each other about how to do a task.
l) Professional historians, mathematicians, linguists, scientists publish papers in journals.
Find some electronic or paper journals. Talk about the format and style. Then get students
to publish their own history/maths/language/science journal as a class – discussing
carefully what should be included. Present these to another class. The journal can be
presented in a “book” format or simply as an interestingly (creatively) displayed set of
pages on a wall.
m) Hold a Maths, Physical Education, Science, Art, Language conference. Students work in small groups to prepare a poster presentation about ideas related to some aspect of the subject discipline. Then invite another class (or parents, or members of the community) to come and look at the posters. If you have access to a hall, gym or other large room, put the posters up and let the invited audience circulate round them, perhaps leaving comments and questions on sheets of paper pinned up next to the poster.
Asking questions
Teachers need to ask questions that encourage students to engage in different kinds of thinking. Ideally, it is useful to use a range of questions from each group below.
Representing ideas
- What could you show me/draw for me to show that you understand X?
- Can you draw a diagram/picture?
- Can you teach that to your partner?
- Can you write that Maths sum or Science formula in words for me?
- Can you think of a problem where people have to use this……………
Classifying ideas
- Can you see a pattern?
- What connections can you make?
- Does everyone in the class/world see this the same way? Why?/Why not?
- What might be the same as/different from…..?
- Is there something here that seems odd? Why might that be?
- What do these things have in common?
Generalising
- What always seems to happen?
- Will this work or is X true every time?
- Can you see the connection between X and Y?
- Can you find one that doesn’t do that/doesn’t work/ is an exception to the rule?
- Is there a rule for this?
Calculating/computing…..
- Can you find a way to solve this problem, work this out, find out what is happening?
- What other ways are there to do X……?
- Is there a quick way to do that?
- Will that procedure always get the correct answer?
Conjecturing
- Can you guess what will happen?
- Will it be the same/different this time?
- What do you think is happening?
- What would happen if we…..?
- What do you think might be the rule for X?
Proving
- How sure are you of that?
- What would you say if I disagreed?
- Can you convince me?
- Can you show me that it definitely will/will not?
- What makes you so sure about…?
Some research results suggest that it is easy to kill off student thinking by saying, “Good”, “Well done”, etc. to right answers. Although students need plenty of praise for their efforts, it is better to do this at the end of sections of the lesson, rather than as a comment to every individual student contribution.
Replace positive verbal cues (‘good’, ‘well done’, etc.) with more neutral, but still positive, responses:
- “Thank you.”
- “That’s a good start.”
- “OK, what else?”
- “Interesting, thanks!”
- “OK, any other responses?”
- “What do people think?”
Try to keep your face neutral for both inaccurate and accurate answers.
Collect inaccurate and accurate answers on the board for discussion.
Ask students to explain why they give the answer they do, whether it is accurate or inaccurate.
Replacing affirming (‘good’, ‘well done’) responses with more neutral ones sends out the message that it is the students’ responsibility to evaluate the accuracy of the work and to keep thinking about it. Having collected a number of student responses, it is useful to:
- Ask the student who gave the answer to justify its accuracy.
- Ask other students to choose the accurate one and justify their choice.
- Vote on them, explaining the reason for the votes.
- Occasionally play the game “Call my Bluff” (Am I really telling you the truth?) and ask some students to try and justify even inaccurate answers and have the other students argue against them.
Praise effective talking on a regular basis and make clear that you view it as work.
Make clear to students that they are jointly responsible for making new ideas by talking
together. Say, ‘Can we make sense of this together?’
Where an idea seems to be understood by one group, but not others, try creating ‘a learning network’ - that is, let students teach each other. Ask students to stand up and move from person to person, teaching them or learning from them each other, using quiet voices. Say, “Everyone must understand together in X minutes. Once you understand, pass it on.” You, the teacher, can check on the learning afterwards by asking students who did not seem to know before to explain their current understanding. (Such learning can also carry on at break time.) Sometimes, students learn better from other students than from the teacher!
Involving everyone
You can help students get involved in whole class discussions by:
- Sitting the students in a circle, or a horseshoe shape, so that they can direct their talk at each other and not just you at the front of the classroom. (Consider re-arranging desks in classrooms if space allows.)
- Slow things down – give students time to think.
- Provide opportunities for students to rehearse (in pairs) before actually speaking.
- Work in small groups for a few minutes where the task is “to make sure that everyone understands”.
- Choosing individuals to respond, but giving them thinking time by asking another question to someone else first. For example, “I am going to ask you about X in a minute Angela, but first I would like to know what people think about…. Y.
- Asking for contributions towards the answer, not expecting complete responses. Ask, “Can you tell me anything about…..?”
- Emphasising that the answer will be constructed from a number of responses and not expecting complete answers immediately. Say, “You’ve made a good start there, who can carry on now?”
- Appointing a student as a ‘temporary chair person’ to manage a discussion, while you keep quiet for a while.
Further examples for discussion
Interactive Teaching in Practice
Year 5 students aged 10: Rounding Numbers
Teacher: Have a look at these numbers (writes 310, 3500 and 6000 on the board.) If I tell you that
they’ve all been rounded in some way, can you tell me how? Talk to your neighbour.
(Paired discussion.)
Teacher: OK. What can anyone tell me?
Fred. That one is 10.
Teacher: 10? I don’t know what you mean yet. Can you say more?
Fred. They have been rounded to ten…. Well the 310 has.
(Teacher nods to indicate that she has heard this and then gestures to the students for other responses.)
Amy That one (she indicates 6000) has been rounded to the nearest 1000.
Jane Yes, thousand…. The 6000 is to the nearest thousand.
Teacher: What do others think?
(There is general agreement from the class.)
Teacher: Can anyone say something else then?
Tony: (Quietly, near the front of the class) The 6000 has been rounded to 1000 and the 3500 is to
100.
Teacher: Did everyone hear that?
All: No…..
Teacher: Can you talk to everyone, Tony?
Tony: (More clearly) The 6000 has been rounded to 1000 and the 3500 has been rounded to 100.
Teacher: What do people think?
(There is general agreement from the class.)
Teacher: OK, we all seem to agree. What I want you to think about is whether it is possible to disagree with this. Can you discuss it again? I want you NOT to agree.
(Paired discussion for a minute)
Mary: (Calling out) It could go either way.
Ian: Yes, 10, or 100. It’s 10 or 100 for 3500.
Teacher: (Waits to see if anything else is said….then) I’m not clear yet.
Ian: What I mean is that you can round 3500 to 10 or 100.
Teacher: What do people think about that?
Fred I think he means that a 6 could go up to 10, which would be 3500 or 96 could go up to 100
which would be 3500 again.
Teacher: (Nods, but says nothing. She indicates that she would like other student responses using her
hands and she steps to one side.)
Rob: Yes, It could be either. Or to the nearest 1!
Fred: No it can’t be. They all end in zero.
Sue: It can only be 10 or 100.
Fred: No… if we had started with three four nine nine point six (3499.6) it would
(General chatter.)
Sue You can’t use decimals.
(General chatter.)
Teacher: Wow! What do people think about that? |Is it OK to use decimals here and to say it was
rounded to the nearest one? Talk about it in your pairs again.
(Children talk and one or two voice their ideas. After a while the general consensus seems to
be that it is OK.)
Teacher: OK. We look like we understand this. Sue, you said that we can’t use decimals. What do
you think now?
Sue: Yes, you can. I can see it now.
Teacher: OK, great! Now, what I want you to do is get together in fourse and practise explaining it.
You’ve got to make sure that everyone in the group understands it and can say it clearly. Use
the 6000 example, then I’ll choose someone to do the explanation. You can use words and
drawings/diagrams if you wish.
When the child presents the explanation, the teacher can use follow-up questions. “How sure
are you? Can you convince us?”, “Can you give us a procedure for working these out?”
Notes:
1. The lesson assumes the students have a reasonable background understanding of the topic, rounding numbers up or down.
2. The problem is presented back to front. Usually students are told to round given numbers up or down.
There is a deliberate element of vagueness: 3500 could have been rounded to the nearest 100 or the nearest 10 if the original number was 3448, say. Similarly 6000 could have been rounded to the nearest 10, 100 or 1000 if the starting number had been 6002. A range of answers is possible. For example, if 3500 was rounded to the nearest 100, then all numbers in the range 3450 – 3549 would be possible. If 3500 was rounded to the nearest 10, then only 3495 – 3504 are possible…. and this implies whole numbers. If you allow decimal fractions to be considered, this provides lots of complexity to consider. The nature of the interactions is worth noting in the text above. Although the teacher still dominates the conversation in terms of the number of speaking turns, there are occasions when several children speak in turn without any intervention. Sitting in a horseshoe or circle, holding back from commenting all the time, using open hand gestures and facial expression to indicate that he/she wants other children to speak, all help the teacher to take an active part in constructing understanding/knowledge.All the teacher’s interventions are based on facilitating the discussion and pointing it in new directions – they do not provide feedback on individual children’s comments. It is the children who are doing the mathematical thinking and not (overtly) the tea
Lesson Plan for Rounding Numbers
| Learning Centre-point | Purposeful task | Interactive opportunities: Getting started | Interactive opportunities: Plenary |
Order familiar fractions and understand how to tell whether range of fractions are larger or smaller than a given fraction
| Create a teaching poster to explain how fractions can be ordered | Write 1/2 on the board. Ask children to call out other fractions. Place them to the right or the left, depending on whether they are bigger or smaller than 1/2. Don’t reveal what you are doing.
Ask children to guess how you are categorising the fractions, explaining their thinking. Ask others to comment on the ideas. Focus on deducing the relative size using number lines, objects and division.
Start again, but this time ask for fractions and place them to the left/right depending on their value in relation to 2/3…. (Tell the students you have chosen a number in your head, but do not write 2/3 on the board.)
Ask students to discuss what fraction you are thinking of and to justify their answer. Ask students what they can tell you about ordering fractions. Gather ideas and, again, ask for comments as you go. Resist the temptation to to too much ‘teaching’ at this stage. Focus on: - “How do you know?” - “What can you show me to help?” - Estimating sizes.
Ask pairs to make a teaching poster which explains how to decide if a fraction is bigger or smaller than another, given, fraction. Give different fractions to each pair, differentiating as appropriate.
| Five minutes before the plenary, ask pairs to rehearse what they might say in explaining their poster.
Choose two posters to focus on first:
- What do we think is effectively done?
- What suggestions could we make?
Place all the posters round the room on the wall. Put a blank sheet of paper next to each one. Ask groups to circulate clockwise round the posters and to leave their comments on the sheet.
Finally, the authors of each poster return to their paper and read the comments.
In another session, authors are allowed to defend their papers verbally. |
