Using Tangram Puzzle as an analog to introduce elements of nature of science (NOS)

State the focus of the workshop and its relevance to the science teacher education.
Despite the importance of nature of science and emphasize on it in Next Generation Science Standards still the question of how the crucial aspects of science can be communicated effectively to teachers and via them to students need to be answered. Among 428 articles published in the area of NOS from 1997-2016 in five science education journals only 3% was about designing and introducing materials and activities for communication NOS. (Nouri, et.al, 2017). Many instructors and researchers keep doing decontextualized activities introduced by Lederman and Abd-El-Khalick in 1998. In this workshop, we introduce an analog to teach different elements of nature of science to preservice/inservice teachers. This activity is unique because of its ability to cover several elements of NOS with doing just one activity. In addition, the materials are very accessible (just tangram puzzle). Since Decontextualized approaches provide a way of introducing NOS concepts prior to exposing students to more contextualized examples (Williams, and Rudge, 2016), this activity can be followed by historical examples to help students to be more connected to the topic.

Explain who within the ASTE membership would be most interested in your presentation (e.g., methods instructors, educational researchers, curriculum developers, etc.) and why.
This is a very proper activity that can introduce many elements of NOS that methods’ instructors can include in their classes. The workshop has been tried in several science methods and professional developments.

Describe the expertise/experience of the workshop presenters to present in the topic area.
One presenter is a science educator with experience of teaching science method class over ten times and her research interest, and dissertation focus is about nature and history of science. The second presenter is a graduate student who is conducting her research in the area of teachers’ professional development in NOS.

List the learning objectives of the workshop and how you will assess whether participants met those objectives.
Participants are expected to learn how to communicate the following elements of NOS using tangram activity and how to support them with history of science. Specific elements that the activity covers include but not limited to:
1. Man is essentially curious and has a tendency to solve the problems that have not yet been resolved.
2. Experiments and errors are considered as integral parts of doing science.
3. The role of luck cannot be ignored in the advancement of science.
4. Scientists’ predictions, background and mentality can be effective in gathering evidence, predictions, theorizing, and so forth.
5. Presumptions play an important role in science.
6. The current incomplete information could lead to the creation of inadequate theories.
7. New information can lead to the confirmation or rejection of an old theory.
8. Scientists make intelligent predictions based on assumptions, and according to the theoretical framework and existing evidence.
9. The formation of a scientific community and a collaborative effort can be very useful in advancing science.
10. How changes in the paradigms occurs in science.

Procedure of workshop
1. Each group will receive 4 pieces of Tangram puzzle (including two small triangles in two different colors, one square, one parallelogram), worksheets, and the instruction specific to their group about their presumptions.
2. The groups are asked to offer a coherent, comprehensive and practical way of introducing pieces, which, at the same time, are highly accurate. Ultimately, we will come to an understanding of the solution, so that all the groups in the later stages will introduce the pieces.
3. The groups follow the instruction given to them in stage 1 and they must complete Section A and B of the worksheet with a discussion in their group. Groups 1, 2,4,5,6 are able to build a rectangular with their pieces. Group 3, needs one more piece to be able to complete the puzzle to reach a symmetry. They are asked to predict all possibilities for this new piece (Refer to figure 1).
Summary of instruction provided to group members.
Group 1, 4 Pre-assumptions (first phase):
– We want maximum regularity and symmetry so you should reach square or rectangular
-You can just have two colors (yellow/green)
-The puzzle pieces can only be triangles or squares
Group 2,5 Pre-assumptions (first phase):
-We want maximum regularity and symmetry so you should reach square or rectangular
-You can just have two colors (yellow/green)
-The puzzle pieces can only be triangles or parallelograms
Group 3 Pre-assumptions (first phase):
-We want maximum regularity and symmetry so you should reach square or rectangular
-You can just have two colors (purple and orange)
-You can use all pieces. You may reach to the conclusion that you need another piece. Predict all possibilities for your new piece.
4. In stage 2 a bigger triangle will be provided to them, and they must complete the part (s) of the worksheet.
Summary of instruction provided to group members.
Group 1, 4 Pre-assumptions (second phase):
-You have a new piece which is fit with your pre-assumptions, so you have to use it.
-Make a new puzzle. Remember you should make it to be a square or rectangular in a way that needs less pieces. You may reach to the conclusion that you need another piece. Predict all possibilities for your new piece
Group 2,5 Pre-assumptions (Second phase):
– You have a new piece which is fit with your pre-assumptions, so you have to use it.
-Make a new puzzle. Remember you should make it to be a square or rectangular in a way that needs less pieces. You may reach to the conclusion that you need another piece. Predict all possibilities for your new piece
Group 3 Pre-assumptions (Second phase):
-You have a new piece which is fit with your pre-assumptions, so you have to use it.
-Make a new puzzle. Remember you should make it to be a square or rectangular in a way that needs less pieces. You may reach to the conclusion that you need another piece. Predict all possibilities for your new piece
5. The groups will be asked to introduce the new piece. In this stage other groups will confront with group three’s problem. Since, based on their presumptions they are not allowed to use one of the pieces, they need one extra piece to complete their puzzle. They have to change their framework. They should predict this new piece but they should make sure this prediction is not conflicting with their assumptions. In the same time, group three recognizes the new piece is fit to their prediction, and complete the puzzle easily. They continue completing the worksheets.
6. All groups in this stage should draw all of their possibilities and predictions in the board. In this stage group 1 and group 2 recognize if they exchange their extra piece (the one that they could not use because of presumption) both puzzles are solved. The same thing happens for group 4, and 5.
7. They would recognize we cannot omit pre-assumptions but we should accept sometimes they limited us. They would see the role of chance, and they understand if a framework is not
answering we have to change it. In addition, different group had same pieces but they reached different conclusion based on their pre-assumptions. They will recognize the role of creativity and science communities.
8. Then we will talk about similarities between doing this puzzle and doing science.
Some possible explanations are:
“Suppose the groups in this class, are the groups of scientists, and puzzle pieces, are the same as the data available to scientists. As a group of scientists, the plan was to make a theory or model by picking up the pieces in your desired frameworks. But what was leading you in your selection of pieces and the shape of the puzzle? Yes, “pre-assumptions.” These mental assumptions of scientists, which are generally called a paradigm, are in fact the set of scientists’ beliefs that emerge from their previous experiences and provides the intellectual framework of scientists to carry out scientific activities.
Compare the first layout of Groups 1 and 2. The first pre-assumptions of the two groups was in common, and this led to the final form of the two groups being the same. But the different second default assumption led them to select only some part of the available data, and as a result, their puzzle pieces were different. Now, let talk about the layout of Groups 3. The rectangular arrangement of group 3 is fully compatible with the pre-assumptions’ of the group and does not need anything else. In other words, scientists in group 3 have come up with a complete model with the help of existing data, but they are convinced (satisfied) of the rectangle’s symmetry. Their model is consistent with existing data and pre-assumptions and is responding to the current issues.
In the second phase of the game, the groups encountered new data. Almost all groups first tried to add new data without touching on the previous framework. But in some cases, this was not possible.
For scientists in group one, two conditions could have occurred: 1. This group, like Group 3, could be convinced of a rectangular model and build rectangles by picking four pieces together. 2. The same group might have concluded that to achieve maximum order and symmetry; they should preferably construct a square. In this situation, they can build the model in a state that has the ability to predict and advance science. With the difference, the model that leads to the parallelogram prediction is dropped due to the incompatibility with Group 1 pre-assumption.
However, new data was not pleasant at all for groups 2 and 3, their model had no place for this new data. Therefore, two scenarios were possible: these groups could have kept their entire rectangular model, which was compatible with their presumptions, and put the new data aside for the benefit of keeping the model. However, they might decide that the existing model, although it was answering to our problems so far, is now inadequate. In this situation, scientists may leave the theory in favor of evidence and build square-shaped models with the above three possibilities. For group 2, a model that predicts a square is excluded because of incompatibility with the defaults.
In the reporting section, by creating a coherent definition for each piece, a common language is created which is accepted by everyone and makes interactions easier. Secondly, scientists (our groups) form a scientific community to provide their scientific achievements. During these reports, the Group 1 presents a new evidence(data) that they did not know its position in science. This is while Group 2 has sought the same evidence and even predicted its features. This interaction, collaboration and scientific exchange can lead to the advancement of science.”
9. Historical examples here will be used to contextualize their learning of elements of NOS.
As an exampleو how central-earth theory changed to Heliocentrism.
10. Groups will answer some questions to reflect on their learning.

Describe how you will make yourself available/offer support to the participants for continuing their learning and collaboration after they return to their home institutions.
All worksheets and complete instruction about doing the activity will be provided to participant. The instruction has lots of picture from different stages. In addition, they can contact us via our emails for additional support.