Game Design for Education (CU Boulder)
Blackboard Learning System (Stanford)
TRAILS and The Math Forum

Responses to 20 Questions! Assignment

Question 3
Name of Assigned Applet
1. Circle Graph
2. Circle Graph
3. Surface Area and Volume
4. Slope Slider
5. Slope Slider
6. Isometric Geoboard
7. Polyominoes
8. Pattern Blocks
9. Slope Slider
10. Isometric Geoboard
11. Understanding Distance, Time, Speed
12. Isometric Geoboard
13. Balance Beam Applet
14. Understanding Distance, Time, Speed
15. Surface Area and Volume

Question 9
Did you encounter any difficulties in working with your assigned applet?
1. Circle Graph: no
2. Circle Graph: no
3. Surface Area and Volume: no
4. Slope Slider: no
5. Slope Slider: no - The applet was nicely layed out. Directions were conveniently placed. The display was easy to read.
6. Isometric Geoboard: no
7. Polyominoes: no
8. Pattern Blocks: yes - One-click per zoom was hard to use. You could simply add a MouseListener to the Zoom In/Out button to handle continuous press. This would be more intuitive for me and many users. No undo was a problem. Couldn't split up patterns once cloned. Zoom in/out had a hidden dependency of resizing the playing field (we lost pieces). Difficult when zoomed out to grab for drag instead of for rotation.
9. Slope Slider: no
10. Isometric Geoboard: no
11. Understanding Distance, Time, Speed: yes - It is not very intuitive. The time control buttons are obvious, but the rest of the controls need to be documented somewhere either in the app (possibly with hovering text) or on the page.
12. Isometric Geoboard: no
13. Balance Beam Applet: no
14. Understanding Distance, Time, Speed: no
15. Surface Area and Volume: no

Question 10
Name three key features of the applet that contribute to its interactivity.
1. Circle Graph
  1. Can enter your own input
  2. Mulitple graphs available
  3. Updates on the fly
2. Circle Graph
  1. The Pie Chart Picture - The Pie Chart picture is important because it gives a visual representation of the data.
  2. The Data Box - The Data Box is important because it gives the user the ability to manipulate the data and receive visual feedback.
  3. The Key (colors, %, etc..) - The key is important because it shows the mapping between the data and the visual representation and breaks down the percentage of the total for each category.
3. Surface Area and Volume
  1. rotation - lets you see the different angles of the shapes and develop spacial awareness
  2. changing shapes - lets you understand the differences between rectangular prisms
  3. triangular prisms changing size - lets you see the effect that various dimensions have on the prism
4. Slope Slider
  1. Display
  2. Sliders
  3. Toggle switches - Each one contributes to the overall effectiveness and interactivity of the applet.
5. Slope Slider
  1. What, How, Why - The what, how, why links are simple and clear.
  2. Display - The display is clear, and nicely illustrative.
  3. Slider controls - The controls are smooth and responsive, allowing for ease of interpretation of the display.
6. Isometric Geoboard
  1. Moving Bands
  2. Clicking and bringing bands to front
  3. Placing Bands on Board - These features allow the user to interact with the applet just like a physical peg board and rubber bands.
7. Polyominoes
  1. Dragging the squares - Dragging allows you to control the position and placement of the squares.
  2. Rotating the squares - Rotating allows different shapes to form.
  3. Grouping the squares together - Grouping allows easier movement of multiple squares.
8. Pattern Blocks
  1. The piece generator - Pieces were a fundamental building block in this applet.
  2. Zoom Buttons - Zooming in and out gave a better perspective and was somewhat playful.
  3. Grab tool - Grabbing to move or rotate was the main interaction mode with existing tokens.
9. Slope Slider
  1. The trace - The trace gave the ability to check against where you just were so you could see how much it had changed.
  2. the intercept/slope sliders - The sliders were obviously important as they are the basic controls of the project.
  3. the changing equations - The changing equations helped link the slope to what we were seeing, it gave real numbers so slope/intercept changes.
10. Isometric Geoboard
  1. Putting "rubber bands" on pegs - The movement of the rubber bands allows students to use the geoboard to build shapes, while the coloring feature allows students to clearly view the polygons which they have created.
  2. removing "rubber bands" from pegs
  3. coloring closed shapes
11. Understanding Distance, Time, Speed
  1. animation - gives the user immediate feedback on the effect the parameters have on the outcome of the run.
  2. popup buttons - the buttons appear to push into the screen when clicked on, letting the user know the app heard her command.
  3. runs fast - there is no lag, so all feedback to the user is immediate.
12. Isometric Geoboard
  1. You can color shapes - This helps you actually visualize the shape you are creating. If you make an octogon and shade it red, it resembles more closely what octogons most often look like in real life to students, and can help them draw real world connections between what they are creating, and what actually exists.
  2. You can overlap shapes - You can overlap two shapes to prove certain concepts (e.g. that a quadrilateral can be broken into triangles)
  3. You can make shapes increasingly complex - I'm not sure that anyone would be particularly interested in making a square, but possible creating a 10-gon or 12-gon could prove of interest to some older students.
13. Balance Beam Activity
  1. Visual effect, idea - The idea of using a balance and the color design of the weights makes it very attractive and interesting to the user. The usage of weights of different shapes, to balance out according to me is a key factor to keep the user envolved and interested in the game.
  2. Analytical aspect
  3. Multiple choice
14. Understanding Distance, Time, Speed
  1. VCR-like controls - VCR controls are comon and easy to understand.
  2. Spinners - Spinners are pretty common, too. The interface is simple and easy to understand.
  3. Animations - Watching the animations is mildly entertaining
15. Surface Area and Volume
  1. Changing the Size - Changing the size is important because you can get different volume and surface area values
  2. Changing the Color - Everybody like picking their favorite colors
  3. Being able to rotate the object - Rotating the object is the most interactive part of the applet

Question 11
Define interactivity as used by your group to answer question 10.
1. Saves time, easy to use, easy to adjust/change data
2. Interactivity is the ability of the user to be presented with a situation, provide input, and receive feedback based on that input.
3. The ability to change and affect things within the game world.
4. The ability to change what is displayed.
5. I started by reading the what, how, and why links and upon learning how the controls worked I imediately manipulated them. In manipulating the controls the response of the graph display was instant, eliminating ambiguity as to my input compared to the output. I would define all of this as the interactivity of the system.
6. The ability to manipulate the objects in the applet in an intuitive way.
7. Interactivity is the concept of having any form of control and manipulation. This includes the available functionalities that allows you to manipulate the environment.
8. The ability of the player to communicate meaningfully with the computer model.
9. The ability to make adjustments in the simulation to control the visual output.
10. "Iteractivity" is something that the user can interact with in any fashion.
11. The ease with which the user can contribute meaningfully to the state of the application and get an immediate sense of what effect she had. Interactivity is a feedback loop between the application and the user.
12. A word describing the ability of a program to change a user's pattern of input based on earlier I/O.
13. Some key features which make the applet very interative to the user and involved in addition to teaching them simple math excercises.
14. I manipulate things in the interface, and the application does something in response that is consistent and predicatable.
15. Being able to change the input to affect the output.

Question 13
Name all the math topics (e.g., fractions) that this applet might support.

Need a list? Refer to: Math Topics List (opens in a new window)

1. Circle Graph: fractions/percentages/ratios, numbers, databases etc.
2. Circle Graph: Finding Percentages, Data Analysis (Circle Graph, Record Data), Probability
3. Surface Area and Volume: Geometry, volume, surface area, multiplication, ratios, proportions, scale, rotations
4. Slope Slider: fractions, linear equations, slope, basic math functions
5. Slope Slider: Fractions, functions, slope, decimals, algebra, derivatives
6. Isometric Geoboard: Convex hulls, Polygons, Graphs, Concavity, Area, Perimeter, Integration, Vertices, Points and Lines
7. Polyominoes: (1.) Geometry (2.) Addition (3.) Subtraction
8. Pattern Blocks: geometry, translations, rotations, measurement, basic shape recognition, tiling algorithms
9. Slope Slider: mostly linear graphing problems
10. Isometric Geoboard: 1.geometry, 2.reflections, 3.translations, 4.coordinates, 5.perpendicular and parallel, 6.congurence, 7.Pythagorean theorem, 8.Polygons, 9.Perimeter and area
11. Understanding Distance, Time, Speed: muliplication, division, linear relationships, slope, distance formula, rate, coordinate graphing, linear equations, variables
12. Isometric Geoboard: Geometry (including Pythagorean Theorem, scale, measurement, shapes, area, etc.), trigonometry, and possibly introductory calulus.
13. Balance Beam Applet: ratio, proportion, patterns,symmetry, measurement, data analysis
14. Understanding Distance, Time, Speed: (1) Equations of lines (2) Positive and negative numbers (3) Ratios and proportions (4) Rates of change.
15. Surface Area and Volume: measurement, linear relationships, scale, perimeter, surface area, volume, variables

Question 14
Using the list of math topics you generated in Question 13
1. Circle Graph
  • young: n/a
  • middle: n/a
  • high: n/a
  • all: all
2. Circle Graph
  • young:
  • middle:
  • high:
  • all: All
3. Surface Area and Volume
  • young: none for just this age group
  • middle: volume, surface area
  • high: ratios, proportions, scale
  • all: multiplication, rotations, geometry
4. Slope Slider
  • young: fractions, basic math
  • middle: linear equations, slope
  • high: none
  • all: fractions, basic math
5. Slope Slider
  • young: (no response from submitter)
  • middle:
  • high:
  • all:
6. Isometric Geoboard
  • young: None
  • middle: Graphs, Area and Perimeter
  • high: All
  • all: None
7. Polyominoes
  • young: Addition, Subtraction
  • middle: Geometry
  • high: Geometry
  • all: Addition, Subtraction
8. Pattern Blocks
  • young: basic shape recognition
  • middle:
  • high: tiling algorithms
  • all: geometry, rotations, measurement, tiling
9. Slope Slider
  • young: 1
  • middle: 1
  • high: 0
  • all: 1
10. Isometric Geoboard
  • young: perpendicular and parallel, perimeter and area
  • middle: perpendicular and parallel, congruence, Pythagorean theorem, polygons, perimeter and area
  • high:
  • all: geometry, reflections, translations, coordinates
11. Understanding Distance, Time, Speed
  • young: multiplication, division, linear relationships
  • middle: slope, rate, variables, linear equations, coordinate graphing
  • high:
  • all: multiplication, division, linear relationships
12. Isometric Geoboard
  • young: Simpler geometry, like shapes and scale
  • middle: More complex Geometry, like symmetry and area
  • high: Trigonometry, Calculus
  • all: Geometry
13. Balance Beam Applet:
  • young: similarity, reflections, rotations, translations, symmetry
  • middle: solving quadratic systems, exponential functions, linear equations, slope
  • high: solving quadratic systems, exponential functions, linear equations, slope
  • all: Word problems of Algebra
14. Understanding Distance, Time, Speed
  • young:
  • middle: Positive and negative numbers, Ratios and proportions,4
  • high: Equations of lines, Positive and negative numbers, Ratios and proportions, Rates of change
  • all: Ratios and proportions, Rates of change
15. Surface Area and Volume
  • young: measurement
  • middle: scale, perimeter
  • high: variables, volume, surface area
  • all: measurement

Question 15
What kind of changes might be made in order to adjust an applet you consider appropriate for young students for use with older students? Would you need to change the functionality of the applet or the accompanying text? Please provide an example.
1. Circle Graph
maybe a more obvious way to change the data names and values. you dont even know it can be modified without accidently clicking on it
2. Circle Graph
We would recommend using different sets of data for younger students versus older students - for example, younger students might relate to a simple example of barnyard animals, while older students might relate better to a table of election results. Neither change would necessitate any change in functionality, just a modification to the built in data sets.
3. Surface Area and Volume
Increasing the complexity of the applet would help make it more appropriate for older students. Right now it is basically just playing with shapes. For example, prompting the user with some more difficult math problem to solve on their own, or perhaps showing how the solve on their own, or perhaps showing how the volume and/or surface area was calculated.
4. Slope Slider
Add more features that increase the complexity, non-linear equations, integrals, trigonometric functions, derivatives
5. Slope Slider
(no response)
6. Isometric Geoboard
Some accompanying text and a goal to accomplish.
7. Polyominoes
  1. Add more complexity and functionality.
  2. More interactive features.
  3. Better graphics is always a plus.
8. Pattern Blocks

The graphics and accompanying text must be suitable for the target audience, otherwise, the applet may be avoided based on appearances or mechanical issues (didn't understand or read instructions).

The difficulty of the game must also be age-appropriate, but some games are able to cater to many age levels, and the core functionality would not necessarily need to be changed.

Not all children's applets can be smoothly and continuously modified to produce older student-based applets.

For example, Bookworm at popcap games could be suitable for children with an appropriate set of graphics and contextual help, however the functionality would not need to be altered.

9. Slope Slider
You would need to have a larger range of functions that you can control with the sliders for it to be beneficial for older students.
10. Isometric Geoboard
Different goals might make the applet more appropriate for older students. For example, if additional features could be added to give side lengths, perimeters, and areas, the isometric geoboard could be used to present a visual proof of the pythagorean theorm to high schoolers.
As it currently is, however, it seems unlikely that older students would get much benefit from this particular applet.
11. Understanding Distance, Time, Speed
younger kids: make the interface more intuitive, maybe with some onscreen instructions
older kids: make it more interesting and challenging by adding more variables such as acceleration
12. Isometric Geoboard
The applet may not need to be changed, but the context in which the applet is used would. For example, a second grader could use the Isometric Geoboard applet to create basic geometric shapes (e.g. squares and triangles) if the accompanying text was changed to highlight this feature of this software. Or, middle school students could use it to create complex shapes to solve Euclidean proofs. The underlying funtionality of the applet does not need to be changed for it to be useful in various settings. Ultimately, though, this probably depends on the applet. The Isometric Geoboard, for exmple, if a very versatile tool, whereas a program that only teaches kindergarten level addition is not. In the latter case, the program itself would need to be changed to increase complexity.
13. Balance Beam Applet
The Graphics! Althought it might be the same problem,concept but the say in this applet I would change the balance and weights designes to make it fit to older students. Older students do not want to play anything which looks like a kiddie game, they tend to be interested in something which deals with stuff that looks older.
14. Understanding Distance, Time, Speed
Non-linear motion. Acceleration. Have the user make predictions about what will happen, then see if they turn out correct.
15. Surface Area and Volume
Change the functionality to have students solve for the correct dimensions for a given surface area/volume or vise vera.

Question 16
A frequently cited design principle involves the importance of helping students make real world connections. Identify three different ways a designer can use with applets and support students to make real world connections.
1. good for business reports/proposals
2. Three different design principles that can help to connect a situation to the real world are:
    The use of real data
    The creation of situations mimicking something that might happen in the real world
    Creating situations in a non-real world context that have obvious parallels to a real situation.
3. Use of a real world example or situation
Integration into a game/puzzle environment that somehow models a real world situation
Giving the user an actual problem to solve, as opposed to just some options to play around with
4. Associate the graphs with real world phenomena.
5. (no response)
6.  Simulations
    Modelling Tools
7.  An applet must provide some functionality or simulation that can be transferred or used in a real world situation.
    The applet must simulate as much detail as possible to the real world application.
    The applet must hold the student's interest i.e. add additional features to make it more interesting.
8. Represent actual objects in the applets, for example, rather than clicking an abstract icon, and having it appear on the play area, they see it get cut out of construction paper... This may make the connection that this could be done in real life, and that the computer doesn't add anything magical.
Adding multiplayer connectivity to an application would allow players to talk about and reinforce ideas presented in the applet.
Identify places in the real world where such concepts have applications, for example, in linoleum design, someone might be faced with this kind of tiling problem.
9. Perhaps putting this in context of graphing a linear word problem.
Having a problem and then having to extrapolate maybe by being able to point to a spot on the line and finding its value to solve some bigger problem.
Could also have the numbers or line change colours when it goes from a positive to negative slope to show when things are increasing/decreasing.
10. This question makes no sense. We both looked at it and neither of us can parse what you are trying to ask. Sorry.
11. graphics of recognizable things help the connection: the runners, the house, and the tree are good because we all know what is being represented. the girl runner is a little ambiguous, though. She should be wearing running shorts instead of a skirt.
animations: these are good because they add to suspension of disbeleif (so users are willing to beleive that the little drawings of runners are really people running, since running implies movement)
use real-world objects and patterns of speech and other things to give the user an identifiable setting
  1. Explanatory text in a tutorial
  2. Create a visual setting in the UI similar to that in which the student would encounter the phenomena in real life.
  3. Use the phenomena portayed in the applet in such a way that models real life behavior of a system. For example, one could create an applet where a student needs to build a tower as high as they can without having it topple. This could help students relate mathematical dimensions with real life stability in architecture.
13. After the applet has been developed, we need to find out the areas in which they are used in the real world. For eg Supermarket (Incase of Balance activity). FInding out if it is applicable in any everyday household affairs. (Kitchen scale) I think that will be the only biggest thing that would help make students make real world connections.
14. Simulate objects from everyday life. Use cultural icons in the program. Ask for predictions from the user about what will happen.
15. Use examples from the real world, ie "we need to build a bridge over the colorado river how much..." Have students take measurements from real world objects and then use an applet to solve something. Make an applet that controls a real world object, such as a robot.

Question 17
What makes this activity fun?
1. interactivity and colors
2. The ability to receive visual feedback based on making numeric changes with a number of bright colors may be somewhat rewarding.
3. It isn't very fun. Maybe just the color changing.
4. Nothing, there are no goals, no association with application, you move a slider back and forth for 2 minutes and you are done.
5. (no response)
6. Nothing
7. Seeing what funny and weird shapes you can come up with.
8. The ability to grow a pattern, and the pretty colors.
9. Seeing colourful things move on your screen while you have control is usually more fun than writing out math problems.
10. We did not find anything fun about the applet, although it is possible that others might.
11. nothing
12. I didn't get any real sense of fun out of the applet. I made a lot of shapes, but I didn't find that particularly interesting. Possibly this would be more fun if used in a classroom setting when following a teacher's instructions.
13. The idea of gussing the weights withough knowing the exact weight of each object.
14. It's not much fun
15. Not much, maybe changing the colors and spinning the object around with the mouse.

Question 18
What would make this activity more fun?
1. Being able to modify what colors are presented. also maybe buttons which allow different graphs to be displayed at the same time such as 3d bar graphs or different histograms
2. Aside from putting it in a completely different context, one fun thing might be to give the ability for the user to manipulate the visualization with the mouse and see the results of the manipulation reflected in the numbers.
3. Some game or problem aspect. Right now its just a visual simulation that gets old rather quickly.
4. Some kind of objective
5. (no response)
6. Anything
7. Understand what else can really be done that does not involve such simplistic actions. What applicaions can be created from this?
8. Adding an optional goal to work towards, suggestions for achieving a goal state.
Little creatures that move around in the play area that can move across the patterns, or interact with the patterns.
Continuous zoom.
9. More ways to interact with the equation. Possibly being able to type in numbers and see the equation/sliders change.
10. Goals! There needs to be something else for students to do besides just making shapes, which becomes boring very quickly.
11. having more controls and choices to make, more information to interpret. perhaps turning it into a game that has winning conditions. a physics/math game where you try to guess how long they will take with given velocity, acceleration, distance, etc.
12. Possibly have a set of goals. Output a specific response when a goal is completed. Give a sense of progress.
13. Making it have different levels.
14. Direct manipulation of the runners
15. Make it into a game where you use the applet to make the correct shapes to solve a tetris like puzzle.

Question 19
What could be done to make this activity last longer?
1. 40 questions
2. We don't believe that there is really any legitimate way to do this beyond putting it in a different context (ie, a class where the students had to analyze dozens of different data sets and answer questions, or a SimCity style game as mentioned before).
3. The game or puzzle aspect that we've referred to in our previous responses.
4. Add some kind of objective that increases in difficulty as the user succeeds.
5. (no response)
6. Specific Goals
7.  More functionality
    More user control
    Some feature involving animating the squares
8. Adding optional goal(s) to work towards, suggestions for achieving a goal state.
Measuring tools.
The ability to resize objects.
9. Similarly to making this useful for older students, a wider range of function options to graph would make it last longer.
10. Additional goals, something that the student would hope to accomplish by continuing to use the applet.
11. (see above - referring to response to Question 18)
12. Once again, a set of goals would be useful. I can only make so many shapes before the program starts to lose its appeal.
13. Levels, different settings each time, more complex sizes and shapes of weights.
14. Direct manipulation of the runners. Acceleration/deceleration. Set up races between the runners, where they start at different places, and you set speeds so that they arrive at the finish at the same time.
15. (see above - referring to response to Question 18)

Question 20
Other comments?
1. (blank)
2. The user interface is generally very nice, though the comma delimited entry of data into the table may be difficult for some younger users.
3. The squares were kind of cool to look at and it was a well written applet, but it doesn't really seem to accomplish any major long term goal. It seems more like a project that you would do if you wanted to learn how to make applets.
4. none
5. (no response)
6. no
7. This applet is too simplistic and doesn't capture any self-interest. This applet may be suited more for a teacher who's trying to teach a student.
8. no
9. This applet was a nice tool to be used to demonstrate a single idea.
Just a note about the questions: Question 16 was a little confusing.
10. The applet is a perfectly functional simulation of what it is supposed to simulate and it was easy to use, but perhaps owing to a lack of familiarity with the educational uses of the geoboard, we were not quite sure _why_ we should be doing any of the things that we could do. Probably context makes this more clear.
11. nope
12. Overall, a very versatile tool. It has many potential uses as a teacher's aide, but would probably not hold a long term educational interest for students left alone to their own devices.
13. I really liked the various topics in math this one applet uses to address.
14. There is potential confusion in that the step specifications are both positive, but the motions are in opposite directions.
15. This applet would require alot of changes to be of use in a classroom setting.

This material is based upon work supported by the National Science Foundation under Grant No. 0205625.
Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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