Choices in Math Class?

Today's lesson was on factoring. Students were shown two methods of factoring. Videos of these methods can be found here:

These methods were meant to give students a step-by-step process to factoring, rather than the old guess and check way.  I told students to use whichever method they liked best. They responded with questions like, "But, which one are we supposed to use on the test?" Again, I explained I wanted to give them options. It was up to them to decide which method they they liked best. It didn't matter to me which one they used.

It occurred to me students are not used to being given choices in math class. They are used to being shown our way of solving problems. On tests, we ask them to show their work, and if their method of solving is different from what we're used to, they lose points. We've taken the creativity out of mathematics. We've made math rigid and have left no room for exploration and discovery. If a student discovers her own solution path, she shouldn't get deducted points. She should be rewarded and praised for her cognition.

Girls doubt their abilities to succeed in "boyish" activities

Today my students in Geometry learned about geometric probability.  By doing a little math, we determined that if an unskilled person threw a dart at a dartboard, there was a 19% chance it would land on a 4"x4" square at the center of the board.  A skilled person however, should be able to beet these odds.

We tested these odds by asking students to volunteer to be in either the skilled group of dart throwers or the unskilled group of dart throwers. Not one single girl volunteered to be in the skilled group. Only boys. I asked the boys why they thought they belonged in the skilled group, and most of them just shrugged and said it was because they figured they were good at it. Then I asked who wanted to be in the unskilled group. Only girls raised their hands.

Were the boys more skilled than the girls? Well, they thought they were. The reality was that neither group was skilled, but the boys were confident enough to believe they could beat the 19% odds. The girls on the other hand, did not have this same confidence.

This activity, meant to teach my students about geometric probability, ended up teaching me a lesson on the self image of young girls. If girls doubt their ability to succeed in "boyish" activities, then what happens when they start to see math, science and engineering as "boyish"? As educators dedicated to social justice, we should be doing our best to make these subject appealing to young girls, and help them to have confidence in their abilities.

Disrupting Class- Guided Questions

Disrupting Class

How Disruptive Innovation will Change the way the world Learns

1. Explain the difference between interdependence and modularity.  How is education currently organized?

Imagine the components inside a cellphone. If the components of a cell phone are interdependent, then each component's design depends on the  design of the other components. Individual designs cannot be improved unless all components of the cellphone are redesigned. Cellphone manufacturers of these types of phones are less willing to make improvements. But if the parts of a cell phone are modular, they can be reconstructed and improved independently of the other parts. This results in companies continuously improving the components of their phones. Currently education is interdependent. Standardized tests require teachers to standardize the curriculum so all students learn the same material. The problem with a standardized curriculum is that it does not meet the needs of each learner. If education were modular, it could be customized and improved to meet the needs of each student.

2. Explain the disruptive innovation theory.  What does this have to do with schools?

Sustaining innovations are products that continuously improve until they surpass the needs of consumers. Disruptive innovation happens when less established companies create a simpler product that better suits consumer needs.

Technology in the classroom becoming a disruptive innovation. Technology allows us to create customized computer-based education programs that can be adjusted to fit different learning styles and different learning speeds.


3.  Why doesn’t cramming computers in schools work?  Explain this in terms of the lessons from Rachmaninoff (what does it mean to compete against nonconsumption?)

If computers are crammed in classrooms to replace live instruction, then they will have no benefit because they are a lesser alternative. Technology will only be beneficial if it is used to fill voids in Education. This is what it means to compete against non-consumption. 

In the 1800s there were no alternatives to listening to live music. People had to pay to hear musicians such as Sergei Rachmaninoff, or do without music. But the invention of the phonograph changed all this. With the phonograph, people could listen to Rachmaninoff's music in their own homes. The success of the phonograph is due to non-consumption. If well-composed live music was easily accesible to everyone, then the phonograph would not have been succesful. But since the phonograph was the only way some people would ever hear Rachmaninoff, it became a success.  


4. Explain the pattern of disruption.

When disruptions first enter the scene they compete against nonconsumption. Disruptions offer consumers a low-cost alternative to more established competitors. Eventually consumers  become aware of these advantages and the disruption gains a higher percent of the market. On a graph were the vertical axis represents the % of the market the disruption is responsible for, this pattern creates an S curve.

5. Explain the trap of monolithic instruction.  How does student-centric learning help this problem?

Monolithic instruction is instruction that is not customized to meet the needs of any particular learner. Often times, educators will try to meet the needs of multiple learners by catering to different learning styles. But because middle schools and high schools in the United States are designed to support  monolithic instruction, the teacher's efforts are usually fruitless. Visual learners will tune out instruction intended for auditory learners and auditory learners will tune out instruction intended for kin esthetic learners.  


If used correctly, computers can support student-centric instruction by meeting the needs of each learner. Student-centric instruction will change students' expectations about education, and pull the classroom away from monolithic instruction. 

6. Explain public education’s commercial system.  What does it mean to say it is a value-chain business?  How does this affect student-centric learning?

In a value chain, value is added to a product in each step of production. In education students are the product and value is being added to them through teachers, textbooks, school culture, administration and faculty. Similar to products in a value chain, each child is given the same treatment before moving on to the next step of production. Value chains are standardized, and in education, they leave no room for student-centric learning.