Perimeter, Area, Volume, and All That: A Study of Measurement

Strategies

Experiential Learning

Learning is an “active and social production”.  For this we need to engage students in “active discussions to help them to create meaning” from their learning.¹⁰   There are many psychologists, sociologist, and educators who agree that hands on learning is essential for learning for most students.  David Kolb is an educational theorist and author who states that “learning is the process whereby knowledge is created through the transformation of experience”.¹¹ His theory consists of four stages that we will use in our unit.  We will actually cycle through the experiential learning model multiple times through this unit.   This unit is so hands on that the strategies are largely student based rather than what I will be doing.  I will be more of a guide.  I believe that it is so important for us, as teachers, to provide authentic practice in “real life situations, not in isolated exercises”.¹²   This method is helpful to not only have the real life experiences, but to make theories of what will happen, plan for action, actively participate in the experience, and then reflect on the experience.

Concrete experience

This is the “do” step.  In the first stage the students are actively experiencing an activity.  Students will first be measuring using rulers, yardsticks, and measuring tapes.  In the next activity they will be using manipulatives to create hexomino patterns.  Then they will be making nets and cubes, followed by paper templates, and then finally making their clay tetradic cuboid.  These are all of our “do” items.  This step will actually occur third, more details to come in the third stage below! 

Observation and reflection

In the second stage (to be completed last) students will practice reflective observation, in other words, they will reflect on the various stages of the project, and observe how they were connected, and what came out.  We will have group discussions about what we measured, how we measured, what problems came up, what our results were, and what we learned using rulers, yardsticks, and measuring tapes.  After creating hexomino patterns, students will take turns posting their forms on the board to see what shapes they did and didn’t find on their own.  We will reflect on how we went about getting the different shapes and how they fit into the area of the enclosing rectangle.  After making nets, cubes, and tetradic cuboids we will discuss why there are only five possible Tetromino forms, but eight possible tetradic cuboids. Note:  We do not count reflections or rotations.  After creating our clay cuboids, we will measure and discuss why the size is smaller after firing (shrinkage).

Forming abstract concepts

The third stage is about thinking.  The learner is meant to create a theory or model of what has been or will be observed.  Even though this is the third step, Kolb makes it clear that the steps can start anywhere as long as they are followed in order from there.  I would like to have students think about what is going to happen before starting working, after a short introduction from me in the form of a mini lesson.  (As I wrote previously, this unit is very student focused and they will be actively involved in each step so my lessons will be short and concise for each activity.)  Making predictions and stating expectations may take away some of the nervousness and anticipation anxiety in students and give them a path to follow.  Even if it is the wrong path, they will discover that and make corrections.  I always tell my students; we have to learn from our mistakes.  Sometimes in art we make mistakes that can’t be fixed and it just leads us down a path we didn’t intend on taking, but may enjoy nonetheless.  Don’t be afraid of change.

Testing in new situations

Although this is the fourth step, it will happen second.  This is the “plan” stage.  Here the students will plan how they will get through the activities.  In the measurement activity, students will know in advance that they are measuring the pool deck, for instance.  In their small group they will need to plan on how that will happen.  Will they break down the deck into smaller pieces to measure or measure the entire area and subtract the area of the actual pool?  Who will hold which end of the measuring tape (if that is the tool, they decide they are using)?  Planning can sometimes be hardest part of getting a job done right, and a job can be completely sabotaged if the planning is not done right from the start. 

Differentiated Instruction

“A fundamental reality in teaching is that our students vary (sometimes widely) in their prior knowledge, skill levels, and experiences, in their interests, and in their preferred modes of learning and way of showing their achievement.”¹³

In my classes I have students who don’t speak English, students who are extremely talented artists, students with outstanding test scores and intelligence levels, students who are delayed in their learning, and even students with physical disabilities that hinder their ability to actively participate in some projects.  However, all these students are able to work and enjoy art class.  This is all due to differentiated instruction.  Not everyone works at the same level, and that is why I must plan for these different levels of ability, comprehension, and interest.  Sometimes, it is just a matter of pairing students with lower abilities with students of higher abilities that are willing to help them out.  Sometimes it is a matter of matching personalities to encourage students that aren’t interested.  Having pictures matched with words in English and Spanish is essential in my room.  For this project we will be using manipulatives (a strategy in itself) so that students with lower skill levels can manipulate the pieces to make shapes rather than being expected to draw them on graph paper (as higher level students will be expected to and all students are welcome to try).  When working with the nets and making cubes, students with physical and mental handicaps can receive a helping hand to get them done.  Most students enjoy working with clay, but varying skill levels means that some students will need exceptions for the forms they create.  Some students may need to be assigned a single cube rather than a tetradic cuboid.