A fun way to develop visual intuition and imagination as well as get some practice with basic arithmetic is to design a dollhouse. If you don’t want to make a dollhouse, bird houses, tree houses, desk organizers, bridges, and entertainment centers are great alternatives.
Here, I describe how we handled a dollhouse design project at Girls’ Angle so that there would be a focus on developing mathematical ability.
For this project to be effective, you should already have a basic familiarity with the kind of object you are going to design. If this familiarity is not there yet, it is important to look at some examples. For a dollhouse, one’s home can serve as a nice example to think about.
Assuming the basic familiarity is in place, one key to ensuring that this project has mathematical value is to design the dollhouse entirely without props. Imagine the dollhouse in your mind and describe it by making a blueprint. By avoiding props, you force yourself to develop your imagination and ability to visualize things in your mind’s eye.
When the blueprints are complete, make a detailed parts list, again, without the aid of props. Making detailed sketches of all the parts requires you to think through the way everything will fit together. You will inevitably want to make sure that various parts match up properly and since you don’t have props to check this with, you will likely have to do some mathematical computations. Incidentally, if you want more practice using fractions, I recommend using feet and inches instead of the metric system.
Only after you have created a detailed description of all the parts should you then build the dollhouse. The actual dollhouse will serve to verify your vision and reveal any errors.
By designing the entire dollhouse before building it, the lessons you will learn from any errors will be stronger. If you instead build the doll house step by step, as you go, it is easy to fall into the habit of making adjustments as needed and there will be few lessons to learn from. For example, if you put the dollhouse together “as you go,” and a wall turns out too short to meet the ceiling, you’d probably just find a wider piece of wood and the episode will slip by without notice.
Try to convince yourself of the validity of your design before construction takes place.
If you find the process of designing without props frustrating, don’t give in to the temptation to design with props. Instead, study other examples more and make your designs less ambitious. There’s no shame in starting with a simple box design. If you are still struggling, take a preexisting dollhouse and draw blueprints for it.
Last spring at Girls’ Angle, a number of girls participated in a dollhouse design project. They carefully drew complete blueprints and made a parts list before we sent all this information to Jane Kostick, a woodworker who makes geometrically inspired wood sculptures and furniture. The reason we outsourced the actual construction of the dollhouse is because we’re a math club for girls, not a shop, so we didn’t want the girls to have to spend time actually cutting out pieces of wood and gluing them together. We wanted to focus on the conceptual problems, not the practical ones. This is not to say that actually building the dollhouse isn’t a valuable process. If you also want to build it, go for it, but stick to your blueprints!
When the finished dollhouse arrived, the girls were surprised by certain features that turned out quite different from what they had imagined. Every discrepancy the designers saw was a valuable adjustment to their inner eye. There were some interesting errors too. For example, the girls designed a beautiful staircase, but when they saw the dollhouse, they saw that there was a missing vertical slat at the very top that a doll could slip through! The mentors noticed that problem but didn’t say anything in order to give the girls the best chance to learn, and, to her credit, Jane didn’t fix it when she built the dollhouse. This mistake reminds me of situations in mathematics where you have to create a list where it’s tricky to figure out where the list ends exactly and you have to make sure that you end the list at just the right place. These girls will be far less prone in the future to the kind of thinking that led to this error.
More mathematics can be treated with this project beyond arithmetic and basic geometry. For example, some of our members designed tessellations for the floors and the roof. You could also include arches and domes and aim for a cathedral instead of a dollhouse. Trinity Church in Boston is an inspiring example of what is possible. You could add more curvy elements such as spiral staircases, elliptical rooms, or walls in the spirit of architect Frank Gehry. Geodesic dome homes are fun to construct and require a good dose of trigonometry. For even more inspiration, watch this ode to Frank Lloyd Wright’s masterpiece Fallingwater by Cristóbal Vila.
Part of the process of developing mathematical skill is developing the ability to imagine abstractly, without props. Much of mathematics is abstract and impossible to realize in a concrete way. Designing a dollhouse in the way just described is an entertaining way to take a step towards abstract thinking.