Primary work has focused on classroom interventions in mathematics and problem solving in middle school 5th-8th grade. Many abstract concepts are grounded in middle school and if these are missed they leave gaps unfilled resulting in children having an aversion of mathematics and weak problem solving ability.
One of the aspects of work has been in making learning math fun and accessible for children while changing the perception of what mathematics is both for children and teachers. I had used puzzles, games, educational material, construction of models, electronics to make abstract learning tangible and provide application for children. This is documented in detail in the CriticalThinking_Report.pdf.
This academic year I focused on extensive use of technology starting with programming with Scratch with 6th-8th graders and mapping aspects of Math curricula through projects and challenges in programming. Three broad approaches were adopted for Math curricula through programming:
- A set challenges for children that involved demonstrating their understanding of abstract concepts visually through programming including fractions, long division, pie charts e.g. demonstrating what it means to add numerator and numerator and denominator with denominator in a fraction and what is a meaningful way to add it.
- A set of challenges were based using programming to understand mathematical ideas visually including linear expressions, percentages, simple and compound interest. As an example 5x+10 was graphed as rectangles of varying heights. Then shapes observed by varying the slopes or varying the added constants were observed and interpretations and explanations explored (stair cases of different kinds including making either the slope or constant a random variable, etc). This was then modified to investigate solutions to equations e.g. 5x+10=75 that used the expression and the pictures and paused when the result was reached.
- Children created games that helped them understand a concept and then work on rigor to master an aspect including positive and negative integers, cube roots that resulted in two digit numbers. Once children get into the mode of creating their own programs often when the computer is available they do not drift and get carried away and play games, they tend to create them. If this is done step by step with values that they put in place first that they knew the answer of and then randomizing it they still want to be able to better their own programs.
Programming was also used in English to give life into the stories that the children had created by animating them in scratch. We worked on this project with two grades 7th and 8th. The 7th graders had also used programming for math and their results in terms of how elaborate and complex they could make their stories even though they were younger and were attempting the stories the first time as well was interesting.
Beyond Mathematics and English, programming was taken further into sensing the real world using Makey, Makey. This helped children respond to a real life event like touching a plant, water or items with some moisture content (not complete insulators). Using this the children made their own version of a water tank filling alarm and a non-touch (pressure based) burglar alarm. These exercises helped children connect the programming to sensing the real world and think of applications where they can make use of these aspects in real life.
To complete the loop of controlling in the real world we also worked with the Finch robot and controlling the actions of the robot to go around obstacle courses and deliver small paper balls into goal buckets. The most popular game we created was the parking game with a random set of commands that made the robot move around and having to predict where the robot needs to be placed to reach a certain goal. We used this version at a school fair with success.
It should be mentioned that this approach is significantly different from ready-made material available for children like online lectures (those available in local language), or animation videos that are more or less passive. The so-called educational games that attempt to 'replicate' rigor use the same methodology of trying to get a high score used in the traditional system with the same pitfalls e.g. if given a choice children play games that they are already good at to get a higher score rather than stretch themselves with new games.
However, a paradigm shift is made when instead of trying to program the child through the computer, we let the children be in control and program the machine. In the first paradigm the computer is always right, the child is always a user and playing catch-up. In the second the children realize that the computer actually needs to be given step-by-step and can't make the simplest connections on its own.
It changes the dynamics of children using machines and their thought process in how they think of an action and break them down. It also helps children truly appreciate the amount of work that goes into making a computer look smart!
More interestingly the children learn a lot of implicit knowledge and conventions by using them e.g. the Cartesian system when trying to move their objects in the directions needed. Children who feel like failures with test scores in time bound examinations, persevere and feel proud when they are able to demonstrate their learning.
We also used physical technology primarily the DIY bigshot cameras that can be assembled by students and over 60 children from various grades assembled the cameras, took pictures and put them on the computer and then used instructions backwards to disassemble them for the next group to use them. The exercise of group work, reading and comprehending instructions and analyzing the pictures was interesting. The hand crank also gave a context to look into gears, ratios. A lot more could be done in optics, imaging. But, the children were very curious about the 3-D images taken by the camera and experimented quite a bit with depth.
The computer lab at Udavi, Makey, Makey, Bigshot cameras and the finch robot were donated by friends and visitors who saw the impact of technology on children and the interesting mathematics that the children were able to do. Further class notes and work of children is available at (www.smallisbeautiful.blogspot.com).
Just as the response of children to technology is obvious so is the lack of teachers who can play with this interesting resource and engage with children. This was especially true for teachers engaged with village children. As part of filling this gap I founded Aura Auro Design (www.auraauro.com) in collaboration with Aura Semiconductor Pvt. Ltd. this year. Aura Auro Design works with 3 electronics graduates and trains them in state of the art analog design (5 hrs a day) while engaging them for (3 hrs a day) to work with schools with a focus on learning through technology.
This has created a small team of local skilled and technically savvy youth who are learning and teaching at the same time. Aura Auro makes explicit that every teacher needs to be a learner.
It has also created a team that is working on STEM research in rural India to deliver results beyond what one person is capable of.