Patterns in Cards Option 2

Patterns in Cards – Option 2

These cards can be used in a longer-term exercise, spanning weeks or months. In very few circumstances are data simply handed to a researcher; more often, they have to actively seek it. To model this, and in conspiracy with faculty and staff, cards may be given to different adults at the school who will relinquish them if asked. These people should be those that it would be good for students to know – the custodian, receptionist, assistant principal, bus drivers, etc. so meeting them is a side-effect of this. It also promotes outreach and social interaction as a way of gaining information.

Suggestion:

1)Divide your class into teams (paper color of cards, or named as appropriate) – yellow, blue, green, etc (you can mark or stamp the backs of cards if you need 2 blue groups)

2)Begin the exercise by giving them a few (2-3) cards, and notifying them that several (5-7) people around campus have other cards for them, and will give cards to them if asked – nicely. They should request their color (and stamped) card specifically and should not see the other cards.

3)There are two upper boxes on each card, and they may be used for (a) initials of the finder, (b) order of discovery, (c) date of discovery, or any other data. It adds other data points for pattern analysis later.

4)Pose a deadline of a few days to gather cards before the first exercise/homework.

5)As they collect cards, have them turn them in to their “file” in the classroom – you can keep track of progress and adjust the timetable as necessary. Students may access their file anytime, but can access other group’s files only with the permission of the group.

6)Assignment: each group should fill in the following sheet, aware that there is more data to gather later, and their findings may be refuted by later discoveries.

Data Findings Sheet 1names:

Group name/color ______date:

1. List the number of the cards (large black number below figure) you currently possess:

1. Observations:
2. What similar traits do the cards share? (list 5)
3. What would you predict about the common traits in future cards?
4. What differences are there between cards? (list 5)
5. What can you predict about future cards?

1. Analysis:
2. Are there any duplicates? Do you expect to find some? Explain.
3. What trends were there in the sequence of cards found? (does the order of their discovery matter?)
4. Were there trends involving the people who gave you cards?
5. What hypothetical “principles” can you suggest regarding the card contents? (are all blue circles odd numbered?)

Consider making 3 “safe” predictions and 3 “wild” predictions, so as to encourage both careful and creative thinking

1. Can you predict a card content (or 2) that you expect to find in the future?
2. What other insights/hypotheses can you suggest about the cards?
3. How confident are you in the accuracy of your predictions so far? (scale of 1-10?) Explain.

1. General questions:
2. How have you worked with or against other groups?
3. What would be the benefit of seeing the cards of the other groups?
4. Are you winning?

Keep the assignment sheets or answer sheets; do not let them revise their answers later.

Continue to distribute cards among new adults, and set another deadline, until the original 19 have been made available. You may also include the bogus cards, but consider making only one available of each type per class. That way, corroborating evidence would exist for the known cards, but not for the bogus ones. You might even produce one with crayon and poor quality and see if they accept it as valid.

At appropriate intervals, have students fill out the assignment sheets like:

Data Findings Sheet 2names:

Group name/color ______date:

1. List the number of the cards (large black number below figure) you currently possess:

1. Observations:
2. What similar traits do the cards share? (list 5)
3. What would you predict about the common traits in future cards?
4. What differences are there between cards? (list 5)
5. What can you predict about future cards?

1. Analysis:
2. How does the latest data change your understanding of the cards? Explain.
3. Can you “discount” or reject any cards? If so, why? Can you justify that decision?
4. What predictions/analyses did you make on the last assignment that you find are not valid based on the new data?
5. What earlier predictions seemed to be most valid?
6. What hypothetical “principles” can you NOW suggest regarding the card contents? (are all blue circles odd numbered?)

Consider making 3 “safe” predictions and 3 “wild” predictions, so as to encourage both careful and creative thinking

1. Can you predict a card content (or 2) that you expect to find in the future?
2. What other insights/hypotheses can you suggest about the cards?
3. How confident are you in your analytical insights at this point? (scale of 1-10?) Explain.

1. General questions:
2. Who, in your group, is the best at finding new data?
3. Who, in your group, makes the most (a) safe, (b) insightful or (c) random or strange predictions?
4. Are you winning?

This assignment can be repeated 1-2 times as more cards are found. Sharing between groups should not be discouraged, but also not presented as expected – see if their competitive instincts interfere with it, and ask them why they continued secrecy having answered question 4a and 4b on the first assignment the way they did?

After 19 cards (20, if you gave out bogus cards), they should be able to organize their cards into patterns or groups. Lay the 19 cards out on a table, so all can be observed easily. Try to organize them in groups in several ways, and describe your grouping (briefly in writing) for each one (like “size of circle”, color, etc).

• Each time you organize them, look to see if your arrangement offers other trends in card data that appear when laid out in that way.
• Note at least three “poor” organizational strategies (which cards you “like the most”, cards discovered by the same person, etc) and explain what makes them poor.
• Look for “useful” organizational strategies – ones whereby you can observe new patterns emerge in other attributes (as black numbers go up, circle size decreases) or missing data (there are three of every star number, except only two of numbers 4 and 5). (do not use these as examples, as they are true relationships that should be discovered)
• Does their useful strategy validate their elimination of earlier cards from consideration?
• Can they effectively (and somewhat confidently) predict the remaining missing cards?

The group should then propose that there is missing data, and explain their reasoning behind that clearly (assignment 4).

Data Findings Sheet 4 names:

Group name/color ______date:

1. List the number of the cards (large black number below figure) you currently possess:

1. Organization strategies:
2. Did you dismiss or eliminate any cards? Explain.
3. What trait(s) are you using as your primary organizer(s)?
4. What trait(s) are you considering incidental or secondary organizers?
5. What supporting evidence is there to justify your strategy of organization?
6. (first)
7. (second)
8. (third), etc
9. What flaws do you identify in your organization?
10. Are any cards “missing”? What data would they contain – be specific (or offer range – between X and Y)?

They should argue from SEVERAL aspects of the evidence, rather than one. They can compare their predictions with those of the other groups, and see whose arguments seem more justified. (all groups should be missing the same two cards). They can use the blank card to produce their “expected” missing cards – useful particularly in the size of the circle they choose, and the color.

Noble Gases:

After that assignment is done, you might not offer the two predicted missing cards (or add them when you’d like) and give out the noble gas cards (three – 20, 40, 84). Ask them how they would integrate these new findings into their pattern of organization. What did they “feel” about the new data initially – were they afraid their structure was going to be found “wrong”? Were they defensive? Did it ultimately reorganize or validate their pattern of organization?

Missing predictions:

Distribute the missing cards (2) from their initial arrangement, and see if they were correct.

Two more rows:

Distribute cards 4 and 86, and ask them to integrate them into their pattern.

What implications does each card offer to your array?

How many cards might there be, ultimately?

Transition metals:

Distribute a few of the additional cards – 48, 52, 56 and see how effectively they can integrate these into their pattern. The insight of breaking the link between “2” star and “3” star cards is not easy to do, but someone in the class should squeeze them in, as their numbers make them difficult to fit elsewhere. You may distribute the other cards (59, 64, 65) as well, perhaps noting that 65 has only one star, but doesn’t fit well with the others.

Hydrogen:

Give out card 1, and ask them the implications of its color and star? (Hydrogen acts as both metal and non-metal)

Final analyses:

What trends can they propose regarding:

a)Black numbers (= atomic masses)

b)Star numbers (= valence electrons)

c)Size of circles (= atomic radius)

d)Color of circles (metal, non-metal, metalloids, colors of Russian flag)

e)Grey line shading pattern (demarcation of metal/non-metal, zentyl line)

f)Green numbers (= melting points, should peak in middle of row, low at ends)

g)Blue numbers (= electronegativities, should trend higher up and to the right)

At some point, discuss the philosophy of scientific inquiry as it relates to this process.

• Do we make predictions with little actual data?
• Do scientific models change over time?
• How quickly did good ideas spread, compared to poor ideas?
• Were some early ideas right on target, but ignored?
• Do scientific models get rejected, refuted or replaced?
• How do we (did they) know that progress is being made?
• How do scientists keep from thinking they know more than they do?

Finally, if no student (or nosy parent) has discovered it, show them a periodic table with the numerical data. The trends they noted are actual periodic trends – clearly presented in the orientation and pattern of the elements groups and periods.

Innovations – like the pattern recognition and predicting two specific undiscovered elements was done by Mendeleev in 1869, and generally accepted within a few years (other groups had similar organizational schemes, but Mendeleev was given credit historically). The red/blue/white circles are homage to Mendeleev’s Russian heritage. His predictions were validated by the later discovery of Galium (1875) and Germanium (1886). The noble gases, isolated in the late 1890’s added a new group to Mendeleev’s table. Moseley (1913) proposed modifying the table to be ordered based on atomic number (not mass, as Mendeleev had done), as isotopes (different mass forms of elements) became understood. Seaborg (1944) proposed splitting the table to insert the trans-uranium elements being discovered through nuclear testing – not unlike “inserting” the transition metals in the simulation.

The results of this exercise are

(a) An appreciation for the process of scientific discovery.

All science does not take place in a 50 minute lab period, and much takes place over years, with inputs from relatively unlikely sources.

(b) A fairly deep understanding of the underlying rationale for the periodic table, without memorizing facts

(c) The sense that different skills of people lead to effective progress – best gatherers of cards, pattern recognizers, predictors, etc are different people/skill-sets.

(d) Collaboration is almost always productive, but not always considered

(e) Strong opinions are as likely to be wrong as right, and the facts will not change to conform to the most dominant viewpoint.

APPENDIX: Prepping the cards before the exercise.

The packets you received contain 42 cards. They should be divided into the following groups:

-4 blank cards – you can offer these to fill in for “missing card” data by groups

-5 Bogus cards – 18 (blue+lt blue/water) 30 (no color/air), 41 (hexagon), 57 (earth), -1 (fire)

-6 Transition metals (48, 52, 56, 59, 64, 65)

-1 Hydrogen – 1 (blue-red gradient)

-Extra 2 rows – 86, 4

-2 Hidden cards – I used 35 and 73, but you can pick two others. I made them consistently missing among all the groups.

-3 Noble gas cards – 20, 40, 84

-All the other 19 – to be distributed as you choose.