Technology and the Future

We had an interesting class discussion around the SAMR model and how technology can impact student learning depending on how it is used in the classroom, which led me to think about the bigger picture: technology is developing tremendously every year and it is definitely going to be a huge part of our lives in the future. So, then how will this affect how people think and behave, and how might technology change people's beliefs and values? Nowadays, many children just don't know what to do without a screen in front of them whether it be a computer, tablet, TV, phone, etc. This actually concerns me quite a lot because I think having too much technology can have some negative consequences, such as lacking social skills. However, on the other hand, could the benefits of technology outweigh the negative impacts and there's no need to be worried about such things? What would the future look like? No one knows the answer, but one clear thing is that human brains will adapt to the environment. The uncertainties can be scary, but exciting at the same time.

I recently watched this video on YouTube: https://www.youtube.com/watch?v=uqZiIO0YI7YHere are some very interesting points:

- today's learner will have 10-14 jobs by the age of 38

- the top in-demand jobs barely existed 10 years ago (iOS and Android developer, data scientist, UI/UX designer, digital marketing manager, etc.)

- we're currently preparing students for jobs that don't exist yet

- those jobs would involve using technologies that haven't even been invented in order to solve problems we don't even know are problems yet

- for the first time in history, we have 4 generations working side by side who are very different in the way they grew up communicating

- lots of data (factual knowledge / content) is available online and the amount of new technical information is doubling every 2 years, which translates to ----> For students starting a 4-year technical or college degree, half of what they learn in first year of study will be outdated by their third year of study

- predictions are that by 2049, a $1000 computer will exceed the computation capabilities of the entire human species

While we shouldn't take all of this information and believe everything that's presented, the video does point out the general trend of where technology might be taking us in the future. Keeping this in our minds, I do believe that we, as educators, need to focus a lot more on teaching students some essential skills that will prepare them for the future:

1. Self-control (quite hard to train with instant gratification kids are getting these days)

2. Critical and creative thinking skills

3. Adaptability to new environments / change

4. Problem-solving skills

5. Love of learning

6. Open-mindedness

7. Being comfortable with complexity and uncertainty

8. Communication and people skills

Are there any other things that I have missed? By the way, how do you even teach these abstract ideas? Through modelling and practicing together? I wonder how technology will change our world in the next 10 years...

My Thoughts on Assessments and "13 Rules That Expire"

Report card time has always been daunting for me because I feel uncomfortable having to put some number on a student and say that so-and-so has or has not met the expectations. What does that number mean anyway? If the student is doing well, then that's "good", but if not, that mark has just killed his / her motivation to try harder next time. I would prefer to only write comments on a report card and not assign any grades. To me, that is more meaningful and valuable than a 50 or a 90. I think we have all been primed to firmly believe that marks dictate children's future because universities have quite high cut-off marks. In that aspect, marks are important; however, we need to look beyond those numbers and see whether children have truly gained the essential skills they need in life. Research has already proven that marks are de-motivators for everyone, so I'm not sure if focusing on marks is worthwhile. I hope that one day, the education system changes so that we don't have to put specific numbers on children's ability.

Now that I reflect back on my teaching practice, I was too focused on generating marks... and I might have done too many assessments. I just wanted to make sure that I had "solid evidence" for report cards but now that I think about it, I don't think those assessments helped anybody. It was reassuring to hear during the class discussion that not many assessments are needed. Despite the complicatedness of assessments, one big thing to remember is this: assessments are there to help improve student learning. Teachers can use assessments to see which area they need to focus more on to ensure students understand the materials, and students can use assessments to get an idea of where they are and ask for help if needed. Other than summative assignments (assessment of), I would rather refer to assessments as / for as feedback.

When Ve mentioned the article, "13 Rules That Expire", I was immediately interested in finding out what those rules might be. Here are the 13 rules from the article (http://www.nctm.org/Publications/teaching-children-mathematics/2014/Vol21/Issue1/tcm2014-08-18a_pdf/):

1. When you multiply a number by ten, just add a zero to the end of the number.

2. Use keywords to solve word problems.

3. You cannot take a bigger number from a smaller number.

4. Addition and multiplication make numbers bigger.

5. Subtraction and division make numbers smaller.

6. You always divide the larger number by the smaller number.

7. Two negatives make a positive.

8. Multiply everything inside the parentheses by the number outside the parentheses.

9. Improper fractions should always be written as a mixed number.

10. The number you say first in counting is always less than the number that comes next.

11. The longer the number, the larger the number.

12. Please Excuse My Dear Aunt Sally

13. The equal sign means Find the answer or Write the answer.

As a student learning math, I remember being taught 9 out of 13 of these rules. (Side note: the article also talks about using the phrase out of to describe a fraction, and it says that the out of language often causes students to think a part is being subtracted from the whole amount. Instead, I should say, "nine-thirteenth". It's scary how our language habits could impact student thinking so much.) This article is very helpful in clearly laying out "expired mathematical language" and providing suggestions for alternative language. As a teacher, I actually feel guilty for having taught a few of these rules and using many of the expired language to the grade 1s I had a couple of years ago. Now that I know better, I can improve my practice and be more consciously aware of how I speak, especially when teaching math.

Rich Tasks

I really enjoyed Wednesday's activity about the coke and super stairs. I found both activities to be very engaging because of the way the problems were presented; they were realistic and relatable. Many, if not most, people have experienced the dilemma of choosing between two different-sized glasses and we all have run up and down stairs.

I appreciate that rich tasks allow all learners to participate and start the question regardless of the level of mathematical knowledge they have. Rich tasks automatically allow for differentiated instruction because of multiple entry points; students can generate possible solutions with their current critical thinking and problem-solving skills. With this approach to teaching math, students would definitely become more willing to think mathematically. They would naturally get curious to know the answer and even if they are not able to get to the solution right away on their own, they will ask their peers and work on the problem together. The skills and growth mindset embedded in these rich tasks are essentially what children need to learn in school.

So, I decided to have a look at some of his videos on his blog. I found the money duck activity that Ve was talking about in class (for those who are interested: http://www.101qs.com/2985-money-duck). This video can start a big class discussion on probability and how the same principle is used to lure people into casinos and lottery tickets; setting a very low probability to win big money but constantly providing small incentives to keep people in. Making these rich task videos might be time-consuming but they are totally worth the time and effort for the education of our children.

http://blog.mrmeyer.com/category/fake-world-math/

In the above link, Dan Meyer talks about the importance of looking at the real world AND real work when making questions. Quite often, teachers - myself included - wonder, 'This is relevant to students' real-life because the question is about cell phones, yet they are still not interested in solving the problem...' Meyer points out that even though the context might be a real-life example, the work that is involved in could be too abstract or computation-heavy, which then quickly leads to students losing interest. This is related to the discussion we had in class about rich tasks having a high applicable context with an advanced mathematical knowledge. I have learned that in order for rich tasks to contain real world and real work, phrasing and carefully crafting the question is the most important task. After all, it is the teacher's job to pique students' interest so that they are excited about learning and enjoy coming to school. As Albert Einstein said, "The formulation of the problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill."

Hmm.. Mathematical Thinking?

Article Discussion: What is Mathematical Thinking?

by Barbara Ball

"A math teacher can decide to spend class time in two different ways: drilling students in routine operations, which would kill their interest and shut down their intellectual development or let them become curious about certain problems they are presented with at the right level, which would help them develop independent thinking skills." This was written by G.Polya in 1944, yet educators still face the same challenge of stepping away from teaching math in a closed way (computation-based) and encouraging students to engage in real mathematical thinking.

'Research on adults born in 1970 shows that their self-esteem and self-confidence at the age of 10 was as important as their academic ability in predicting later achievement." So, instead of killing students' interest, educators need to foster an environment where students learn to enjoy doing math. We want to raise kids who can think independently and critically so that they are able to solve problems in the real-world whether it be a simple task of choosing which detergent to buy to a complicated task of deciding which stock to invest in later in their lives. In order to do that, we need to define what mathematical thinking means and what its implications are in math education.

When engaging in a mathematical task, it's important to focus and pay attention to what we do before presenting a possible solution. The thinking that happens during the process is very valuable in developing critical problem-solving skills in students:

                - identify a task or situation to explore

                - break down a task

                - identify similar tasks which may help

                - identify appropriate knowledge and skills

                - look for a pattern or connection

                - identify assumptions

                - select a strategy that might be appropriate

                - consider alternative approaches

                - formulate a conjecture (a theory / guess)

                - test the conjecture and reformulate if necessary

                - prove the conjecture

                - make connections

Words That Describe Mathematical Thinking	Example Prompts
Exemplifying, Specializing	Give me one or more examples of... Describe, Demonstrate, Tell, Show, Draw, Find
Completing, Deleting, Correcting	What must / can be added, removed, altered? Tell me what is wrong with... What needs to be changed so that...
Comparing, Sorting, Organizing	What is the same and different about..? Sort or organize the following according to...
Changing, Varying, Reversing, Altering	What if...? Do... in two or more ways. What is the quickest, easiest...?
Generalizing, Conjecturing	What happens in general? Is it always, sometimes, never...? Describe all possible... What can change and what has to stay the same so that...is still true?
Explaining, Justifying Verifying, Convincing, Refuting	Explain why... Give a reason... How can be sure that...

The activity involving snap cubes that was done with a group of educators at a conference get at the heart of developing mathematical thinking skills. A teacher's role is extremely crucial: What kind of questions are you going to or not going to ask? How are you going to word those questions? How much guidance will you provide? It's not a matter of how difficult the required computations are to solve a problem, but how much demand there is on a high level of mathematical thinking that goes into formulating a final answer.

Dan Meyer points out how we can get through many math or physics textbooks just by using decoding skills. I also fell into this trap and used to think that I could "think mathematically" really well when all I ever did was pull out the numbers in a word problem and plug them into a formula to get an answer. When I was challenged with real questions, I felt frustrated and often resorted to leaving it up to others to solve the question because I just wanted the answer. This goes back to the idea of people being "impatient with irresolution". As a teacher, one thing to keep in mind is to ask the right probing questions to get students curious and thinking about how to approach problems so that they can formulate their own conclusions through patient problem-solving. I truly believe that if you're equipped with creative critical thinking skills, you can overcome a lot of difficulties that come your way.

Discussion Questions

1. Prior to discussion: What is your definition of "thinking"? What is thinking? What do you think is "mathematical thinking?"

2. What can we do to promote mathematical thinking? More importantly, how can we get students to become interested in math in the first place so that they are willing to think about it?

3. From the article: "The more children are tested and graded, the less motivated they become." We want to encourage kids to develop and practice critical thinking skills, but we still live in a society where people are graded and evaluated upon certain marks (e.g. SATs for students, LSAT and any other standardized exams for various professions). What is your opinion on standardized testing?

My group talked about many different things; what do we think mathematical thinking means, using more of open-ended questions and parallel tasks to promote critical thinking skills, how standardized testing can put some challenges for educators but also be used to check and reflect on teachers' performance as a whole. We came to a common understanding that mathematical thinking skills are not only applied in math, but it's also about developing transferrable skills which can be used in many different areas when problem-solving.