Doolittle: Off the grid

After reading this article, my first stop was that we are so obsessed with grids that we are following the same structures and schedules again and again instead of seeing its failures. But this is not the same with Indigenous cultures, they are not so obsessed with the grid. They have their own natural ways of understanding the situations. It is very important for us to understand that one can tackle some of the failures of the grid but one can not change everything according to himself or herself.

We are only teaching Euclidean geometry in the schools, but there are some other ways as well those can be used to teach concepts in geometry and algorithm. For instance; Knots which is ancient Indigenous tradition of string figures and it is related to three-dimensional geometry of space.
I really like the indigenous people's agricultural tradition of farming without using clocks and calendars and also their definition of territory. Indigenous people like to go with the flow of nature instead of trying to take everything under control. There are a lot many things one can learn from indigenous culture.

We should look beyond the fixed grid and try to see the situation from different perspectives, and should also use alternative geometries, geometries of liberation into our math classrooms.

The wine and rat puzzle

Rat 1 drinks 1-100
Rat 2 drinks 101-200
Rat 3 drinks 201-300
Rat 4 drinks 301-400
Rat 5 drinks 401-500
Rat 6 drinks 501-600
Rat 7 drinks 601-700
Rat 8 drinks 701-800
Rat 9 drinks 801-900
Rat 10 drinks 901-1000
one of them must be die, and the bottles remains to test would be 100 now
Rat 1 drinks 1-10
Rat 2 drinks 11-20
Rat 3 drinks 21-30
Rat 4 drinks 31-40
Rat 5 drinks 41-50
Rat 6 drinks 51-60
Rat 7 drinks 61-70
Rat 8 drinks 71-80
Rat 9 drinks 81-90
Now there are two possibilities, if the one of the rat dies drinking these bottles then there are only 10 bottles to test, otherwise the poison is in remaining 10 bottles
If the rat dies, there are 10 bottles to test again
Rat 1 drinks 1st bottle
Rat 2 drinks 2nd bottle
Rat 3 drinks 3rd bottle
Rat 4 drinks 4th bottle
Rat 5 drinks 5th bottle
Rat 6 drinks 6th bottle
Rat 7 drinks 7th bottle
Rat 8 drinks 8th bottle
we have two remaining bottles, if one of the rat dies than it is clear which bottle is this. otherwise 2 rats can taste remaining bottles and we can check which bottle is poisoned.
This same phenomenon could be used to check the second possibility.

Unit plan and lesson plan: Draft 2

https://drive.google.com/open?id=165DAdZr1mx2MOtG5bQbKKXTZzIh3pySE

Draft unit plan and lesson plans

Below is the link to my unit plan:


https://drive.google.com/file/d/165DAdZr1mx2MOtG5bQbKKXTZzIh3pySE/view?usp=sharing

Thinking about math textbooks

As a former student, I loved to use textbooks. My teachers taught me according to the textbooks. It was very easy for me to follow the structure of the textbooks. I read the definitions given in the starting of the lesson, then I looked at the examples to understand the use of formula to solve the questions. It was very easy for me to solve the worksheet questions by following these two steps. Although I was not able to solve all the question, I needed help of my teachers to understand certain questions. As a teacher, I noticed that it is not easy for each students to understand mathematics by just seeing the definitions and examples given in the textbooks. Moreover, the textbooks usually have 2-3 examples those are not enough for students to understand the whole concept. Linguistic used in textbooks also sometimes confuse students. Moreover, sometimes examples are given as the perspective of others, and students don't feel connected to them.
Previously I thought that textbooks are important for students as they get to know what they are doing, but now my perception has been changed. Now I think that when teachers follow everything given in the textbooks they become so dependent on them. They don't want to try different activities those increase the critical thinking of students. The school, I went for my short practicum doesn't use textbooks. The teachers only get the idea from textbook about the topic, then they plan their own activities, and worksheets suitable for that topic. The activities they choose are connected to the real life situations, and students like to discuss those activities with their peers and teachers. I observed that students learn better in this way. I think this is the reason schools nowadays trying to adapt new techniques of learning  instead of making students text-books dependent.

The Scales Problem

A market vendor sells dried cooking herbs in whole-number amounts from 1 to 40 grams. The vendor has an old fashioned two pan weigh scale, and has exactly four weights of different amounts that allow them to weight out any of these amounts of herbs--without using the herb or any other object as an auxiliary weight.
According to me the values for 4 weights should be 1,2,5,10. When I saw this problem, it reminds me of Indian weight system. Most of the vendors in small cities use two pan weight scale to sell their fruits and vegetables. Although they have more weights, and their weights usually include 1,2,3,5,10,20,50,100. According to me suitable weights those add up to the numbers from 1 to 40 are 1,2,5 and 10. I didn't take 3 because to get 3 we can add 1 and 2 together.
1,2,5 and 10 can add to get any value up to 40. For instance
1gm= 1gm                                                                                                    
2gm=2gm
3gm=1+2
4gm= 1+2=3 and again plus 1gm
5gm=5gm
6gm= 5+1
7gm= 5+2
8gm= 5+2+1
9gm= 5+2+1=8 plus 1gm more
10gm= 10gm
11gm= 10+1
12gm=10+2
13gm= 10+2+1
14gm= 10+2+1 plus 1gm more
15gm= 10+5
it would continue like 10 more than as from 1 to 10
we have to add 10 twice to the calculations from 1 to 10 to get the numbers between 20 and 30, and thrice for numbers from 30 to 40. For instance, 37=10+5+7 once and again add 10 two more times. It is possible to get any number between 1 to 40 by using these four numbers.
Are there several correct solutions?
Yes, there might be several correct solutions to this problem. The other numbers should be 1,3,5 and 10 or 1, 2, 10, and 20. But according to me one number must be 1 and the second number must be either 2 or 3.
Extension to this problem
What should be the 4 weights if the vendor wants to sell dried cooking herbs in whole numbers amount from 1 to 100 grams? Could you use the same weights as you used for 1 to 40 grams? why or why not?

How to promote flow in classrooms

It is very important to maintain flow in our classrooms. It plays a vital role in the development of growth mindset, which is very important for every student to be successful in life. Flow means to completely involve someone in what he or she is doing. To create such an environment for students so that they just fully concentrate on their work instead of keeping track of time, which students usually do when they feel bored in the classrooms. Now the question here is how we can promote flow in classrooms. 

Open ended questions: As I learned in our problem solving class, always give students an open ended questions. Don't tell them that the question has only one particular answer. Let students try different methods to solve the problem. Be ready to extend the problems. Students feel excited in solving these type of problems.

Check prior knowledge: Before giving any question always check the prior knowledge of the students. Challenge them according to their skills, because if we will give hard tasks to the students they will feel anxious and bored. The question should not be too easy or too tough. 

Not tell too much: Feel free to share the relevant information as long as the question remains problematic for the students. Do not share too much information with them.

Clear instructions: Always give clear instructions to the students such as how they will solve the problem; in groups or individually. What the question is. What strategies they need to follow to solve the problem.

Connect problems with their daily lives: Always try to make problems relevant to their daily lives. In this way they feel more connected to the problem and try to solve it with more enjoy and curiosity. 

Personal interest: Check the personal interest of students and allow them to choose activity of their own interest. Always make your students feel comfortable in your classrooms, so that they don't hesitate to share their problem with you.

Moreover, involve them in hand on activities because students learn more by visualizing things. Last but not the least take them to the gardens to teach which would be very helpful to maintain the flow.