Session 5.3 - Collecting and interpreting information: Part one
Learning intentions and objectives.
In this session you will learn about:
- using short enquiry tasks to introduce the idea of enquiry based learning to your students
- collecting and interpreting data in an enquiry-based lesson
- the importance of recording the results of enquiries
- collecting accurate and reliable data
- preparing for an enquiry-based learning session through a series of lessons and a ‘project day’ or ‘field trip’ for maths or science classes
Success criteria.
To meet the learning intentions you will:
- review a short perimeter and area enquiry task on Geogebra
- complete a simple data collection exercise on personal profiles
- watch a video as a stimulus for discussion on encouraging students to record their findings during enquiries
- watch a video sequence illustrating a procedural error and refine resources and data collection process to minimise such errors
ICT components.
The ICT components you will focus on are
- GeoGebra, perimeter and area.
Also, as in the previous session, you will continue to apply the ICT skills you have learnt so far for EBL, and to think about how they help you implement EBL in the classroom.
Resources needed.
Resources needed for this session:
- Papers of different sizes (at least two pieces of paper for each teacher),
- Different coloured pens (at least one for each teacher),
- Computer/laptop/netbook and the Internet.
AUDIO
Student motivation
Priscillah tells us about her surprise that even students who would normally be disengaged during lessons were able to draw correct conclusions during an enquiry into soil amounts/types and water retention.
Priscillah speaking about student motivation during a science investigation.mp3, 01:33,(Series: OER4Schools audio, episode 01)
1 Review of follow-up activities from last session
If you are running a professional learning programme which follows these sessions in sequence, then you should do the review of follow-up activities relating to the previous session (test). The 'review of follow-up activities' for that session is available here, and also shown below in the session text. However, if you are following selected sessions in a different order, then you should use the reflection appropriate to the previous session you did.
The review of the follow-up activities for this session (to be done at the start of the next session) is available here.
There is no review of follow-up activities from last session available. You can go to the previous session (OER4Schools/test) and create one.
2 Further tasters of EBL: Investigating perimeter
Same-task group work (15 min) on investigating perimeter.
Working in your small groups of three to four participants, complete the following activity (the applet will open in another window when you click on it) which uses GeoGebra. In this activity, we would like you to experiment with drawing figures with different numbers of squares (you can click and drag them into position) and observing how the perimeter changes.
Take some time to explore the applet and think about the type of enquiry that it lends itself to (demonstrated enquiry/structured enquiry/problem-solving enquiry/independent enquiry) and how you might use it with your students. Do you think the results table is a useful addition to the applet? Share your findings with the other participants and share whether such an activity can be used in the class as a taster of what EBL is about.
You may like to refer to the following guidance notes for some ideas on how to make use of the variety of perimeters with fixed area GeoGebra resource:
1) Overview
After learning the concepts of perimeter and area, it is easy for students to think that figures with larger perimeters would also have larger areas, and vice versa. This applet helps teachers to explore with students the variety of the perimeters of a figure formed by several congruent squares touching side by side. Together with the complementary applet Variety of areas with fixed perimeter, teachers can clarify with students that a figure with a larger area may have a smaller perimeter, and areas and perimeters are two different concepts.
2) Learning Objectives
- Recognise that figures with the same areas could have different perimeters.
- Recognise the strategy of minimising the perimeters of figures with the same areas.
3) Teaching Approach
An enquiry teaching approach is expected. Students are asked to arrange 3 to 9 squares to form different figures and find their possible perimeters. Teacher then guide students to express their strategies of getting the largest and smallest perimeter with a certain number of squares.
4) Teacher’s Note
For each number of squares, ask students to record the possible perimeters in the table of the applet. Guide students to focus on the change of the perimeter when a square is dragged to a new position. Discuss with students the strategy of minimizing the perimeter, especially for 4 and 9 squares.
Note that while the instructions for the task are short, it will take some time to complete the task. Make sure you limit the time appropriately, so that there’s enough time for the remainder of the workshop.
The following task may be used as an alternative if preferred or if there is no GeoGebra resource:
Investigating volume and surface area of paper boxes
Each group of participants should have access to papers of different sizes. Each participant should fold a paper box using each of the papers. Use an appropriate method to measure the area of paper and volume of the paper box. Would the size of the paper affect the volume of the paper box? Or would it be dependent on how you fold the paper? What is your initial ‘best guess’ or hypothesis? How will you go about finding out whether your guess or hypothesis is correct? Share your findings with the other participants and whether such an activity can be used in the class as a quick taster of what EBL is about.
3 Simple data collection exercise
Same-task group work (10 min) on data collection This is a fast and simple activity in which you (or your students) fill in the blanks, and you learn more about each other. On a piece of paper, draw a simple profile of yourself (forehead, nose, mouth, and chin). You and your group members should choose at least four items from the following list of possible information about each other, and write them inside the profile using coloured pens:
- Name
- Favourite time of day
- Favourite colour
- Favourite sport
- Favourite subject
- Something I did that I'm proud of
- Birthplace
- Something that makes me laugh
- Favourite food
- Favourite animal
- Favourite song
You can post the profiles in the classroom or create a display section in a suitable venue in your school along with your picture (or your students’ pictures). For another variation, you can use a spreadsheet, to consolidate a particular aspect of the profile of the class (e.g. favourite time of day, favourite food). These can be shown on a regular basis as ‘data’ from your class. (e.g. My classmates all like to eat ’nsima’){|}{Kenya My classmates like ugali}
Now try to come up with some interpretation of the data from all the profiles in your group.This is a great way to get to know each other and also the group as a whole.
4 Collecting and recording data
Whole class dialogue (10 min) on data collection. Data collection is an essential part of many EBL activities. It is important that data is carefully and accurately collected. Otherwise, the interpretations and conclusions you draw from your enquiry can be very misleading. For instance, you would not want your profile in the previous activity to contain any mistakes about yourself. Some common methods of data collection include:
- Reading reference material in a library or on the Internet
- Conducting an interview
- Using questionnaires
- Doing an experiment.
Discuss with each other whether you are familiar with each of these data collection activities.
It is important to give students ownership of how they prefer to collect and record their findings by giving them options to choose from. It is also important for teachers to discuss with them the reasons for collecting or recording findings, because they may not understand why they need to collect or record findings in a particular way.
Now watch a video clip on Nixolo helping students to collect data in her EBL lesson and bear in mind the following questions:
- Why do you think it is important for students to record their findings during the enquiry process?
- Are the students in the clip motivated to record their findings?
- Can you think of ways to help the students engage with the recording information part of the enquiry process?
VIDEO
Recording findings
Recording information during an enquiry. Noxolo encourages a group to record their findings. She checks who in the group is supposed to keep the records of the investigation.
Video/Noxolo 3D shapes 1.3 AfL3 recording.m4v, http://mws-93306.mws3.csx.cam.ac.uk/wiki/Video/Noxolo_3D_shapes_1.3_AfL3_recording.m4v,This video is available on your memory stick in the video/3D shapes folder. Duration: 0:40 (Series: 3D shapes, episode 13)
Discuss the questions as a whole group and record any interesting or useful observations in your notes for this session. Here is a copy of the worksheet that the students in the video are completing:
Students in the video are recording information on polyhedra such as number of sides/faces/vertices etc. By recording these in a table next to the name of the polyhedra (which they have build as part of the investigation) the students will hopefully be able to see patterns emerging both within each data set and between data sets.
5 Information gathering and data collection
Recall the five enquiry ideas (A-E) that were discussed in the last session.
Enquiry ideas
Idea A: Investigating paper airplanes
There are many different designs for paper airplanes. Some of them have a very plain design but can fly a longer distance whereas some can have a rather interesting design but not fly as well. What are the factors that affect how far a paper airplane can fly?
Idea B: Investigating the process of hand washing
We have been told that washing of our hands is an important part of maintaining hygiene and preventing the spread of germs and viruses. How do you know that you have spent adequate time washing your hands each time?
Idea C: Investigating the vegetables and trees within our community
What are some of the vegetables and trees that are grown in our community and why are they being grown here? (e.g. consider tomatoes, rape, onion, cabbage, nimu tree, holy fiso, malaina, mango) Some possible areas of investigation: location of vegetable/trees (e.g. type of soil and availability of water source like stream), medicinal properties (e.g. is it used as a traditional medicine?), nutrition properties, economic consideration (e.g. source of fuel/income), ecological and environmental concerns, personal and spiritual values.
Idea D: Planning for a trip to the game reserves and Akagera National Park
Imagine you have two overseas visitors who have just arrived in Kigali and would like to visit a game reserve near Kigali, plus the Akagera National Park and one other interesting site by car. The two visitors only have one day to visit these three places by car. Can you inform the visitors about the distance to these places from Kigali city centre? Can you also suggest an itinerary that will take into consideration the shortest distance of travel to and between the three places, starting and ending at Kigali city centre? Please state the distance of travelling to each place and the approximate time required to travel.
Make sure that you do consider the practical arrangements for this trip! In the itinerary: decide on the length of your imaginary journey and work out the travelling time, but also think about the practical arrangements: how much luggage (water, food, equipment) will you need to take and how will you be able to carry this? Are there any elderly people or young children in your party, who might need special provision, such as extra food, or more frequent stops?
Idea E: Investigating my body and how it works
Children are naturally curious about how their bodies work so this is a rich area to draw on for enquiry ideas. For example:
- pulse rate and how it varies with exercise
- lung capacity and how it varies with height/sex/pulse rate/chest circumference
- BMI and being healthy
Get back into the groups that you formed to work on a few of these ideas during the last session. We will assume your group has been able to develop one or two of these ideas into enquiry-based lesson(s) and you now want your students to start collecting data to answer the enquiry questions.
Same-task group work (10 min) on data collection Discuss in your groups the following questions:
- What form of data collection will the students need to work on? Do they need to identify sources of information or conduct some sort of experiment or calculation?
- If it is a form of experiment or calculation, do they have the necessary skills or knowledge to conduct the experiment or calculation? How will they record their results? How will I make sure to integrate ICT into this process? Would the use of a spreadsheet help students to keep track of and if necessary further process results?
- If it involves identifying sources of information, where do they find the information? How do they know the information is valid and how can they access the information?
- What other ways of finding information are there?
- Consider whether or not it might be useful for students to make a prediction of what they think the outcome might be.
In the next session we will consider making predictions and hypotheses again and build on the introduction given here. Encourage students to look up the NRICH article linked to below - they may even want to spend some time exploring the site for some useful mathematics enquiry ideas.
Making predictions
Simply put:
- a hypothesis is an explanation of why something is happening (or will happen) and so is a good starting point for investigation/argument/further observations/tests
- a prediction is a statement of what you think will happen before it does so
It is possible to make a prediction based on a hypothesis or without a hypothesis.
You can read about hypotheses in more detail in this NRICH article on understanding hypotheses.
Encouraging students to make predictions about the outcomes of their enquiries allows them to exercise higher order thinking skills as they must think about the many possibilities that might occur/exist.
An enormous amount of valuable, deep and exciting information is available on the Internet, but an enormous amount of total nonsense, falsities, half-truths and unsupported theories is also out there. Your students have to learn to distinguish between the two, but you cannot give them hard-and-fast rules. Everything that comes out of an established publishing source isn't good information, and everything that comes from a personal home page isn't bad information. The kinds of things that students ask may be answerable only by other people, perhaps only by a knowledgeable person other like a teacher, parent, medical specialists, etc.
Same-task group work (5 min) on collecting data for analysis. After the discussion, assess if the resources that you have prepared so far would be adequate for the students to embark on the data collection process (whether it is in the form of experiment or enquiring through the Internet/asking people). If not, make some changes or consider creating additional worksheets or perhaps a spreadsheet for the students. If you would like your students to make a prediction and/or form a hypothesis, make this clear on your worksheet. You should make sure that you have included an ICT element in each of your enquiry ideas.
Observing, thinking, reflecting (5 min): Video sequence and discussion.
Imagine that you are the students who are going through the data collection process.
Watch the following video sequence of some students collecting data for an enquiry into BMI and being healthy (Idea E). The students have been collecting data independently and the teacher has noticed a problem.
VIDEO
Collecting accurate data
Judith shows pupils again how to measure their height accurately, emphasising the importance of using the correct method and paying attention to detail. Using a straight tape measure that starts at the floor (at zero), Marsha measures 1.45m.
Video/Judith body A06.m4v, http://mws-93306.mws3.csx.cam.ac.uk/wiki/Video/Judith_body_A06.m4v,This video is available on your memory stick in the video/Judith body folder. Duration: 1:04 (Video filmed in 2012, at CBS.)(Series: Judith body, episode 06)
VIDEO
Checking for anomalous results
Judith draws the pupils' attention to differing height measurements for the same pupil. Using this tape measure, Marsha measures 1.29m.
Video/Judith body A07.m4v, http://mws-93306.mws3.csx.cam.ac.uk/wiki/Video/Judith_body_A07.m4v,This video is available on your memory stick in the video/Judith body folder. Duration: 0:51 (Video filmed in 2012, at CBS.)(Series: Judith body, episode 07)
VIDEO
Collecting data for the BMI enquiry
Judith guides pupils to help each other to discover the source of an error when measuring height.
Video/Judith body A08.m4v, http://mws-93306.mws3.csx.cam.ac.uk/wiki/Video/Judith_body_A08.m4v,This video is available on your memory stick in the video/Judith body folder. Duration: 1:44 (Video filmed in 2012, at CBS.)(Series: Judith body, episode 08)
Try to anticipate where these types of problems (procedural errors) might occur as you collect data for your 'idea' in the following activity. It is likely that you will need to refine your data collection procedure in a similar way that you have just refined your resources in the previous part of this activity.
As an aside: Once your students are used to working in the spirit of enquiry you can pose short enquiry problems to be solved for homework or at various stages of a lesson. For example, the teacher in the above clip might have asked the students to work out a solution to the problem of the measuring tape not starting at the floor with the proviso that the solution should not include measuring Martha again or moving the measuring tape. The answer of course is to measure the gap between the tape and the floor and add this to Martha's incorrect height measurement. By giving the students a few minutes to discuss the problem in groups of three or four, they may have come up with this (or perhaps another even better) solution - students can sometimes surprise us with their ingenuity. Once the size of the gap has been worked out, this result can be added to all other measurements carried out using that tape - the students will see this as a worthwhile exercise because it means that they don't have to measure everyone who used that tape again!
Same-task group work (10 min) collecting data for analysis.
- Now go ahead and complete the experiment or data gathering part of your chosen enquiry. Try to come up with joint predictions and/or hypotheses and make sure that everyone in your group plays an active part in collecting the data.
- By the end of the workshop, you should have the full data set and findings that you could share with the other groups next week.
Some post-activity questions for discussion (if there is time):
- What other kinds of challenges can you anticipate your students will face when completing this phase of the enquiry-based learning lesson?
- How can you support your students as they face these challenges?
- Does the use of ICT in your activity support students’ learning?
6 ICT practice: Making use of ICT in enquiry-based learning
Different-tasks group work (20 min) with ICT for EBL. You now have acquired a large range of ICT skills (images, slideshows, the browser, GeoGebra, spreadsheets, Etherpad for collaborative writing, concept mapping, online simulations, typing). You've also had the opportunity to deepen your knowledge and skills within one particular application. We now turn towards using these applications for EBL.
Think about all the applications you have encountered. How can you use those applications in EBL? Think about the concrete projects that you have developed with these applications and consider:
- the level of enquiry they promote
- ways of extending/differentiating the level of enquiry
- how user friendly is it for yourself and students
- how engaging will it be for the students
- the relevance to your teaching subjects or curriculum in general
Continue to develop some new activities for classroom use, bearing in mind the above list. Develop detailed activity plans and share and test your ideas with other participants. As always, try those activities in the classroom.
7 Connecting with overarching goals of the programme
Open space (10 min). It's now time for the "open space", that gives you an opportunity to discuss issues that have arisen, and to relate those to the broader context of the programme. Do not just gloss over this section, but make time to raise issues, and probe the progress that you are making. You could use this space to:
- Remind yourselves of the of the Most Significant Change Technique, and e.g. collect more of your stories.
- Discuss your assessment portfolios: Is there anything that you are unsure about? Is it going well? What could be done better?
- Check on the work with the classroom assistants: Is this going well? Are there any tensions? Any observations or tips you can share?
- Reviewing individual ICT practise (such as typing practise).
- If you are preparing a presentation for other teachers, you could work on the presentation (about what you have been learning, stories emerging from MSC).
- Remind those who are doing audio diaries, to upload them.
- You could discuss any other issues that have arisen.
You will find notes and summaries of various techniques and concepts on our reference page, and you might want to refer to those for clarification during this activity if needed.
8 Follow-up activities
Agreeing follow-up activities (5 min).
Participants should set concrete days for their GeoGebra day, as well as for the project day. Part 1 of the investigation should be carried out between 5.4 and 5.5. As you go through the homework, explicitly discuss days or lessons which teachers can set aside for this.
Part A: Try out in your classroom the same mini-GeoGebra enquiry as in the first taster EBL activity above, with learners working in mixed groups of 3-4 around a computer. Consider the following question: how did your students respond to the open nature of this task? What other observations can you make that will help you evaluate the use of GeoGebra to explore this topic. Note down the responses and observations. In the next session you will share this with the others.
Part B: Continue to work on planning for a ‘project day’ or ‘field trip’ and share any development of ideas in the next session. It may be that you have introduced some form of EBL whether in the form of a mini EBL (as in Part A of this homework) or the ‘project or field day’. Be ready to share the positive, minus and interesting (PMI) points that you have noted so far when introducing EBL in your classrooms. The following additional set of questions can be considered for thinking and sharing of PMI, if you have already started to make use of EBL in your lessons:
- How are the students involved in framing the enquiry tasks and questions? (e.g. could groups or individuals generate and record ideas about "what I/we want to know"? Or in the case of a whole class investigation, could the class vote on which enquiry is the most interesting yet feasible to pursue? )
- Are the tasks open-ended enough so that students could also take some responsibility for how they develop, rather than just producing an answer or a solution? (open-ended tasks can still contain guidance)
- Can students conduct an experiment, search for information or resources themselves?
- Can students interpret the information or data themselves?
- Can you persuade students to ask more questions without feeling shy or stupid?
- Can you show students that you can be a learner alongside them?
- Are the resources - inside and outside the classroom, human/material/digital - sufficient and accessible to all of them?
- Can you, and the rest of the class, give comments or criticisms that are constructive and sensitive? Can the group be encouraged to take on board constructive feedback?
- Are the students motivated to suggest more enquiry ideas of their own?
In the next session, these follow-up activities will be reviewed. If you are using this session on its own, you can have a look at the review of follow-up activities here.
At the end of each session, we provide an overview of the activities in this session, together with their suggested timings. Although this appears at the end of the session (for technical reasons), you should keep an eye on this throughout the session, to make sure that you are pacing the workshop session appropriately!
Total time: 100 (min)
Activities in this session:
- Same-task group work (15 min) on investigating perimeter.
- Same-task group work (10 min) on data collection
- Whole class dialogue (10 min) on data collection.
- Same-task group work (10 min) on data collection
- Same-task group work (5 min) on collecting data for analysis.
- Observing, thinking, reflecting (5 min): Video sequence and discussion.
- Same-task group work (10 min) collecting data for analysis.
- Different-tasks group work (20 min) with ICT for EBL.
- Open space(10 min).
- Agreeing follow-up activities(5 min).
If you have printed this session for offline use, you may also need to download the following assets:
- Video/Noxolo 3D shapes 1.3 AfL3 recording.m4v (local play / download options / download from dropbox)
- Video/Judith body A06.m4v (local play / download options / download from dropbox)
- Video/Judith body A07.m4v (local play / download options / download from dropbox)
- Video/Judith body A08.m4v (local play / download options / download from dropbox)
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