The End of the Line…For Now

What a season, what a season. If I were in person for this blog, I’d probably applaud myself and cheer rather pathetically, as is my style.

This blog post is designed to be your one-stop shop for all of my learning project posts in case you ever need to lose a few hours to me bumbling around, trying to find math in the most interesting places. All baking related, of course. I learned a lot in the ten posts that I made during this project, and I got to eat and share a lot of yummy things, too!

My friend, my sister, and I made pies this weekend, and I instructed both of them on how to properly mix the custard-y fillings, and how to make whipped cream. And how to separate eggs, so I really did feel that I made progress in my cooking. My sister even said, while we were baking, that she thinks I have come along way because I no longer look terrified when I am baking something. So that’s a plus! Below are the blogs I made wherein I learned to bake.

 

One-Stop Shop for all Your Blogging about Cooking Needs

  1. Intro – the first thing I did was decide that I was going to bake for this project. Honestly, I mostly just wanted to eat tasty things and tell everyone it was for a class. I didn’t expect much from it other than that. I added in the mathematical knowledge on top of it, for two reasons. As I mentioned in the post, I did do a baking project with my Grade 8s (I saw all of them a week ago, it was amazing, but also sad because I missed them so much, and I wish I could just stay there, but alas, I have to Film Festival it up, yo), but also because I wanted to prove to myself that I could find math in anything, and make it tangible and worthwhile to me and to my imaginary students.
  2. Salted Caramel Cookies – in my first post, I started with cookies becuase I thought it would be easiest. But it turns out I actually learned a lot from the experiement. I learned that cookie dough thickens depending on the temperature and the amount of flour proportionally, and that caramel like, evaporates in heat. For this math lesson, I did Grade 8 proportions, based on those two learnings.
  3. Salted Caramel Cookies – Revised – this post was more for me to actually learn from my mistakes of last time, and to try something new. That is, to put more caramel in smaller balls of dough. Not a complete success, but definitely an improvement.
  4. Cheesecake Brownies – I learned that my biggest impedement to cooking is my self confidence, as evidenced by my being wayyyy too stressed about how long to bake the brownies for. I decided to then make the math lesson revolve around Grade 9 linear realtions so students could find ways to graph and understand those baking times I struggle with.
  5. Cupcakes – This was when I made so many cupcakes it was like, the worst decision, there were 60 cupcakes, send help. The learning I did here was incredibly valuable, because it helped me gain confidence in my baking skills. I had to work hard and perservere when my recipe for the fillings didn’t turn out. And I learned to trust my judgement and not be afraid to try new things. Once again, my math lesson revolved around my learning and mistakes, with it being Pre-Calc 20 linear inequalities, and working with adjusting amounts of variables in an equation to make the best baking even if the recipe asks for different numbers of cups or amounts.
  6. Cake – Super fun one where I baked with my Mom. I love my Mom, she’s great, and she was a big help in me making the cake that I always make her make me for my birthday. Not much learning here, except again, gaining that confidence with baking times. I decided that the math could fall into Workplace and Aprenticeship 20 or 30, with surface area and volume. Mostly because it facinates me that the poke cake increases it’s surface area with the holes, but decreases its volume.
  7. Cooking Videos – The week of no kitchen because my parents were doing renovations. So I watched some videos to help inspire me for weeks to come. This blog will forever be known as The Time that Sarah Decided She was going to Separate an Egg and Talked about it for Literally a Million Years before She Actually did it. I hope I capitalized appropriately there.
  8. Pie – Probably where I learned the most, to be honest. I learned about how pie filling thickens, and to trust the recipe when it tells me these things happen. I learned about how meringue is formed by egg whites, and I learned how to make every part of a recipe from scratch. This lesson was for pi day, and so I used Pre-Calculus 30 as my lesson, as I thought it would be kind of cool for students to use a pie to introduce and look at the unit circle. Not because of any actually mathematical relevance the pie would have, just because it would look cool and be fun to cut in to.
  9. Brownies – The time I lost a bet and had to blog about it, because it involved baking. The best part of this blog was that I got to take one of Carmelle’s awesome suggestions and make it – which was the best idea! The Oreos in the recipe made me think it would be cool to ask Grade 7 students how many cookies could possibly fit into the recangular shape without losing any part of the cookie. Of course, you can break the cookies and reshape them. But in my math class, we don’t waste any of that cookie, it goes on that brownie.
  10. Mousse – The be all end all of the project. I learned to separate an egg (I DID IT) and I learned how to fold in ingredients. It was a super fun part of the project, and I felt like I had actually learned a lot when I got to this point. Especially in the way of confidence, because though I thought I had failed, I just kept trying, and working at the recipe, where in January, I would have just given up and asked someone to just do it for me. So that was the biggest step of all for me. I also learned a little bit about baking and how air is useful in baking. I am still not 100% sure how mousse is made, but I do have some better ideas due to the beating of the eggs and heavy cream.

So that’s it! There’s the whole project! I hope you enjoyed being a part of the learning, and I hope  you try out some of the recipes yourselves. If you take anything away from this experience, I hope it’s what I learned the most – to be confident in yourself and just keep trying, because failure is not the worst thing.

Oh, and also, math is totally everywhere, I bet you can find it. Learning is everywhere, I bet you can find it.

 

Have a great, amazing, splendid, and worthwhile day, you are all wonderful humans, probably.

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Inspiring Creativity through Education

I have a lot I want to talk about and this will probably all be a huge mess. I apologize in advance for the slog this will be. I will try and break parts of it up with photos or videos if possible!

…buuuut it’s still going to sort of be a wall of text, so I don’t blame you if you take a pass on this one.

This week, we talked about some of the “hot button issues” related to technology in education and what our own opinions and experiences led us to believe on the topic. I admit that I am far too passionate about this, so this is why it will indeed result in rambling, but I chose to comment on the discussion we had in class surrounding the question of why we teach what students can Google, and the question if curriculum needs to be abolished or changed altogether with the rise of technology and information being readily available at our fingertips.

My opinion is this. I think we should by all means be changing how we teach and how our students learn with the changing environment of our world. I believe that the way we have taught for years is not the best way, and is not the system of success, but the system of the privileged, and the system of the mundane. We do not teach students to learn, we teach students to recite. And this is why I think that technology can shape the world for the better by forcing us to not teach our students what can be found on Google, but instead to teach our students to Google, to be curious, and to want to learn.

         This photo is a gift from me to you called “I      searched creativity on Google with photos that are               allowed to be shared and this is what I got”

         What is the Problem?

School Kills Creativity

I know I saw Ken Robinson’s TED Talk on this topic in my first year of University, so I’m pretty sure I’m not the only one who has seen it, but I think this video works nicely as the opening point to my opinions on how our education system perhaps does need to change and be adjusted to account for some of its failings.

Here is the video as well, if you want a YouTube video, instead of the TED Talk website.

Basically, the idea is that school encourages students to stop trying new things, to stop thinking outside the box. He states this by talking about how young children are unafraid of being wrong, and are unafraid of failure. And then we give them the consequences for failure that mean that they’ll never want to not succeed again.

And while it is true that failure needs to have some form of acknowledgement, it doesn’t mean that students need to feel as if they are a failure simply because the answer was incorrect, or different than expected.

We teach students that there is only “yes” or “no”, and there is no “maybe” or “let’s try it” or “what about this?” and, in doing so, we give them that black and white idea that one is good and one is bad.

I think that absolutely school kills creativity and it is our job as future teachers to do something about it.

Behind Every Successful Person there is a Feeling on Education

Now, I don’t want to make it seem like I’m being a terrible person, and I’m not saying that education is terrible. Because honestly, I read through about a million different quotes from famous or “successful people” and what they had to say about education, and I disagreed with a lot of what they were saying. So I am perhaps providing a bit of a biased look by choosing the quotes that prove my point, but I admitted to it, so you all know that there is a large amount of bias being shown all over this blog.

But I want to emphasize why I chose to include this part. I made this choice because if our education system was perfect and the way we have organized the system worked then there wouldn’t be legitimate criticisms of the system. Everyone’s heard the list of people who dropped out of high school or university to move on to greatness – Bill Gates, Steve Jobs, and Mark Zuckerberg, to name a few straight, white males – and people use them as examples. To let people know that they can achieve greatness, that they can do good things, that they are capable of anything, no matter their grades or how they did in school. We hinge self-worth and importance on school, we elevate people by their perceived genius because they excel. But then when we take a look at the people who have played a large part in what has made the world what it is today, we see so many of them denouncing the education system.

It is, in fact, nothing short of a miracle that the modern methods of education have not yet entirely strangled the holy curiosity of inquiry; for this delicate  plant, aside from stimulation, stands mainly in need of freedom; without this it goes to wrack and ruin without fail. It is a very grave mistake to think that the enjoyment of seeing and searching can be promoted by means of coercion and a sense of duty. – Albert Einstein

The fact that ideas, that inventions, that science, math, poetry, everything in the world was discovered and created due to someone having an idea or a passion is no secret. Math spent most of its time being manipulated by people with the desire to see more. Scientists like to blow things up in the name of SCIENCE, poets like to see if they can write a poem about having no meaning and artists like to see if maybe driftwood has a hidden figure in it somewhere.

My point is that a lot of what we teach students in classrooms today was discovered by someone who wondered why. Who asked questions. Who tried things. Who failed more than they succeeded. And then we sit there, and tell our students they are destined for greatness. They are destined to be like the ones they learn about who created everything they love. And then we teach them in a system that does not nurture and cultivate the skills needed to do the things they did.

By the way, random aside, I was trying to find the poem I was referencing up there. I could not find it. So maybe Google is not that useful after all……..

Here is, from her best recollection, what the poem sort of looked like in my sister’s memory. Not totally related, I just promised there’d be pictures, so here’s a screenshot of my skype.

         What Happens Next?

 

 

Rediscovering Mystery

Those of you who are in my EMath class already heard me talk about this, so I apologize for the repetition. I found a documentary online the other day, called Rediscovering Mystery. Gonna give my props to Danny O’Dwyer, the video game journalist and documentary creator who made the documentary. He left his old job to start a Patreon so that he could make an in depth series of videos that explore the inner workings of game creation and development. He’s really awesome, you should check him out, look at his YouTube channel if you have any interest in video games in general.

But even if you don’t, you should totally watch the documentary on mystery.

The reason I include this is because I find that the lessons highlighted in the video can also be easily drawn to education and how we should be adjusting, shifting, and changing our direction in teaching. They talk about how creativity in games is dead because of the rise of the internet and strategy guides and FAQs on the internet meaning that it is easier than ever to just give up on a puzzle. They talk about how game development has moved in this direction as well. That if a player can’t solve a puzzle in five minutes, the game will pop up a little hint at the top directing the player. Games hold the player’s hand to an extent where no one wants to figure things out on their own anymore. And the developers discuss how they made their games – Frog Fractions, The Witness, and Spelunky – in spite of these stipulations. All those games are amazing, by the way, check them out. Frog Fractions is also free, Just saying.

In school we hold our student’s hands. We give them hints if they get stuck on a question. We give them a step-by-step guide to do a math problem. We give them multiple choice on tests. And when a student gets something wrong, we shut that line of thinking down, sometimes before they even get to their wrong answer. We work so hard to garner student success instead of thinking about how success should look and feel.

This is why inquiry in the classroom is so important. Because it encourages students to try things, to experiment, to not worry if they get the answer wrong, because often, there is no one right answer. I am a fan of this idea and this doctrine because we are then teaching students to not be ashamed of something that they’ll spend more of their life doing. The majority of people (like, I’d say over 90%, but that’s a made-up stat, sooooo) fail more than they succeed. It took me a long time to learn to make mac and cheese. I still am not a perfect baker, but I can make a mean meringue, who knew? You start every task with attempts and losses, and you work toward the success that means you’ve mastered a skill, idea, task, or concept.

That is what the documentary is alluding to with solving puzzles and mysteries in games. Games like The Witness give you no walkthrough, just a very simple straight line of about five or six puzzles before the game literally opens up into an entire world and you can go wherever you want. I spent my first four hours of the game literally wandering in a village where I didn’t solve a single puzzle because I had unwittingly found the area of the game you should probably do last. The game has puzzles you can go the entire game without seeing, and it blew my mind when I knew there was so much more to explore (literally so much, you can beat the game in the first ten minutes, and like, who knew?).

Frog Fractions has that last idea in it. That there is so much more to it than meets the eye. It is not what you think it is. And sometimes you can play the game and never move past the first section because you don’t know what the game is hiding. And Frog Fractions 2 is so crazy, I can’t even describe it.

Spelunky has a secret boss that is literally an eggplant monster that is literally so impossible to get to, only one person has ever done it without a partner, something even the creator thought was impossible.

That was the obligatory games rant. To show you the lesson these games can teach us.

  • You can figure something out even if someone doesn’t give you guidance or instructions
  • You can try new things and see what works
  • Not everything is how it seems, and sometimes you need to look at information from a different angle to see the bigger picture
  • Something may seem impossible, until you try hard enough

Technology and Exploration

We give students opportunity. We stop using our curriculum to create a hive mind with singular opinions and ideas and instead we teach our students to explore, to want to learn, to desire the answers, to fail, to learn from their failures, to then succeed.

From failure you learn. From success – not so much. – Aunt Billie, Meet the Robinsons

Technology gives us immense opportunity to work with exploration in the classroom. Like, I said earlier, give them a reason to Google, instead of teaching them the facts they can look up.

Here are some of the ways that technology can help us in devising change and opportunity in our curriculum, and how we can rediscover that mystery that is missing.

  • We can use the internet to explore math games with students – my table group and I looked at two websites yesterday in my EMath class – Math Hombre and Plastelina that have various math puzzles to explore and learn from.
  • Of course, there is Desmos and all the graphs you can explore there, and the art you can create.

  • You can do a flipped classroom and have your students watch the content of your class at home, and come to school for help or enrichment – gives you more time in the classroom for exploration, challenging questions, real life applications, and trying new things with the work.
  • You can use resources on the internet to find more interesting and creativity inducing lessons – use pinterest, twitter, any resource that will share ideas with you.
  • Encourage students to use Google, to look up things in class when you don’t know the answer, to research for an inquiry project responsibly.

These are my ideas on how we can instill creativity and mystery into our classroom, on how we can still use our curriculum we have, but teach it in new fun ways that inspire students to fail more than they succeed because that failure is worth it. There is something worth learning in being wrong. That even though you can Google something, doesn’t mean you know the context, or know why it is important. It is up to a student, a class, and/or a teacher to tell us why what we’ve Googled is relevant, and where we go from here.

That was my blog, if you made it this far, you are a very determined soul. I apologize for the length.

Getting Creative With Assessment

It seems that a common, underlying theme I have found in most of my education classes is creativity. It is never really stated – we don’t have an “Intro to Creativity Class” or an assignment requiring us to showcase our creative soul or anything. But I have found that it is essential, if you want to do well as a teacher and as a student learning to be a teacher, to be creative. Forming lessons that encapsulate an outcome or big idea in a way that promotes student understanding, creating math questions that challenge students but also breed inquiry, adding Treaty Education into every subject in a wholesome way that does not damage the integrity of the subject. And creativity, have I ever found that creativity is essential in working with assessment.

There are two types of assessment that I really want to focus on. Particularly because I feel like they are not always done well in classrooms, and I really do think that they are important, because I think that knowing how to guide your teaching is such a simple way to show students that you care about them, know what they are struggling with, what they excel at, and are tailoring your unit and lessons to them and their abilities. The two I want to focus on are  diagnostic assessment and peer/student assessment.

Diagnostic Assessment

In my EMath classes, we have been learning about the Five Practices and how to teach mathematics in a way that promotes student understanding first. Students are encouraged to solve an open-ended, or open-middled questions in any way they see fit. There is not one way to tackle the question and, in some cases, not one way to answer the question. The questions have many access points so most students can even simply get a start on the question. An example of a lesson I have written using the Five Practices can be found on my blog. Anyway, one of the first parts of creating the lesson is anticipation, coming up with multiple methods that could be used by students to tackle the question and what barriers/questions may be encountered when using the method.

Anticipation is always the most difficult part of doing the Five Practices for me, because it’s hard to think in more than one way. But this is where diagnostic assessment really comes into play. Once you know your learners, and you know them well, you will learn what kind of minds they have, how they think and what parts of their math skills are stronger than others. And once you know all that, you can start anticipating with more and more accuracy. And getting to know your learners can be accomplished through diagnostic assessment.

Diagnostic assessment is a way to pre-assess students, show what they know and where their strengths lie. In ECS 410, we can up with a list of many different ways to pre-assess students, and the ones that I was the most intrigued by to try in a math class were the KWL charts, a cardstorm activity, and a modified version of a quiz, or test.

KWL, or Know, Want to Know, and Learned charts are interesting to me for the same reason that the cardstorm activity is. One thing that we seem to let slip when we teach a subject, any subject really, is the understanding part. We often think it’s enough that a student can do well on a test, tell us what 2*2 is, write out the year the war of 1812 took place in, write a poem that includes synesthesia, or draw a hydrogen atom. But the question ends up being did they just rote memorize what they thought would be asked of them, or did they really understand what they were learning? Can they tell me what it means to multiply numbers? Can they tell me why poets use synesthesia in poems? Can they tell me why the hydrogen atom is drawn as it is? And that is where I really find an activity such as the chart or the cardstorm are useful.

They make students put into words, or descriptions, what the math really is and what it means to them. It shows their thinking of a certain concept. When you do KWL chart, it shows what the students want to learn, so it gives you a place to start in your teaching. It gives you what interests students have in that particular concept.

When you do a cardstorm, you allow students to group together all of their words, symbols, pictures, and phrases and give each grouping a title. Having students explain their thinking in the groupings as well as which sections are their favourites and least favourites help you as a teacher to see which areas of a concept are their interests, or what they understand, as well as which areas they may be struggling or disinterested in.

Both activities are also useful in that if a student cannot articulate or explain any pieces of the concept that delve into the meaning of the subject, then they do know have that understanding, and must then be taught it.

The first two really give a clear picture of students’ interests, disinterests and understandings, but the quizzes are where student thinking is apparent.

Using a quiz with multiple open ended questions that all relate back to the core concept being taught are really what I think tests are for. Tests shouldn’t necessarily be marked – that way a student is not afraid to write whatever they are thinking or however they are solving a question, and they are also not afraid of getting the answer wrong. The quiz is also useful to the teacher, because it shows them they ways in which students instinctually answer a question. Adaptations should be made for students if they need it, because it will help accurately show exactly how that student learns. I, for example, would have much preferred to be able to talk during tests. It didn’t need to be to someone, I just need to voice my thoughts aloud to hear if what I’m thinking makes sense, and logic out the question. If a student needs that adaptation, it is helpful to know that ahead of time before it becomes a problem later.

 

Student/Peer Assessment

When I was in class, the only time we were given toward student or peer assessment was either when we were self-correcting tests, or when the teacher paired up students who were struggling with those who were more advanced and got them to help struggling students. While I do think that both are useful methods of student/peer assessment, the way in which we did them didn’t do much help. The marking was done with the teacher giving us detailed instruction on how to mark the tests and there wasn’t really any room for students to use that assessment to better themselves, we had already done the test, and so we were simply evaluating our mistakes, with no chance for improvement. The second was done with the teacher literally outlining that the “smart kids” would be helping the “not-so-smart kids”. Which is a horrible thing to say, because I don’t necessarily believe that a student can just be labelled, or written off, before you learn exactly why it is they are struggling.

In Making Classroom Assessment Work, there is a section on self-assessment that demonstrates why exactly it works using a line with loops in it. It shows that, when a teacher assesses regularly, there are many loops. But, if a student and their peers also assess the work of a student, the number of loops can double or triple. And while a teacher can only assess once in a period of time, the teacher can have students self and peer assess before they hand in assignments to be assessed by the teacher in order to have the students get two more chances to make sure that the work is meeting all of the expectations of the assignment. And what is also noted is that the students and the teacher came up with the expectations together.

I think that giving students the chance to do that last chance assessment is really useful, because there are a lot of little mistakes that we cannot see ourselves in our work that a fresh pair of eyes could easily identify. Maybe we copied a question down wrong, maybe we forgot that our teacher prefers we don’t use contractions in formal writing. But also, before we give it to that peer to look for those mistakes, we ourselves also get a chance to make sure that we are comfortable with having others assess it. Sometimes, having that pressure of immediacy, of having the assessment be directly after we hand it to the peer will be just the incentive needed to look over that paper, that assignment, that picture we drew one more time to make sure we are proud of it, or accept that it is our work.

I know that when I do work, I often feel so burned out by just finishing it, that I can’t imagine reading it all as well. And, like most, procrastination is my friend that tells me I can just put an assignment off until the last possible moment, and it’ll be all fine. Giving students that time to look it over, to have it emphasized to them that they should look specifically at how their work matches up with the rubric before passing it to a peer to do the same gives them that time, that opportunity to do the work they didn’t find time for at home.

The final point I want to address about self-assessment is the metacognitive part of self-assessment. Self-assessment makes students think about their thinking. In the text, it mentions that students who have no extra support in the classroom may really benefit from using metacognition, because it helps them to reflecting on how they learn, which they can then articulate to the teacher, so that the teacher can teach them better.

As I mentioned before with the Five Practices, knowing the way your students think is extremely useful in the classroom. And getting students to help you identify what type of learner they are, and how they go about solving problems can help a teacher help their students all that much more. Like with the loops, a teacher can only get so much done in the time they have, so having students do some of the work themselves can save a lot of time, and also be beneficial to the students.

The biggest thing I would have students do to self-assess in math would be to have them outline why they answered questions the way in which they did, or why they decided to use that particular approach. Like I mentioned, I think it is essential to have students understand what it is they are learning, as well as why they are learning it, and as the target in the assessment text shows, when students monitor themselves, know the language of assessment, and are invested in learning, they can be lead to understanding all that much more. Having students articulate why they multiplied two numbers together shows that they understand what it is that multiplication does to numbers and how it is necessary in a question. On the flipside, it may also show them that it doesn’t make any logical sense for them to have added two numbers, and so, they need to look at how they solved a problem again to maybe edit it.

 

The importance of assessment is shown in the growth that students can have the opportunity to make when the direction of the learning is geared toward their previous understanding, and also in the way that students get a chance to think about and understand their thinking and the thinking of their peers. If students are involved in their assessment, they are involved in their learning, and it makes the lesson we agonize over stick, and it makes the learning feel important and involved to the student, so that they have responsibility and autonomy over some of their learning process. So, how will I involve all of this assessment in my classroom? Well, to tell you the truth, I have many ideas, like some of the ones I outlined above, but I am still growing, and still learning. So I will just have to learn more, get creative with I learn, and change my math classroom, or any classroom I have into one that has more than just tests and quizzes.

Insight and Creativity

The third EMath class I attended moved from the class being focused on the difficulties and conflicts which arise when dealing with problem solving, and instead brought to light many positive approaches to problem solving as well as why the practice is useful to students and teachers alike.

The first activity we did involved many brain teasers and questions, like where we had to draw four straight lines through the box of nine dots without lifting our pencil, and completing the magic square. The activities involved a lot of free thinking, and discussion, as we worked on the activities in groups. The questions were simple and straight forward, we understood what was expected of us, but we were encouraged to come to the conclusion on our own, and through our own devices. For example, the first activity we did involved finding numbers in the boxes at the top of the page, and counting them off in order. The event was timed, and we were required to record and plot our data. The process was ended when the instructor could see that frustration levels were beginning to outweigh our enjoyment. The activity brought up the fact that problem solving in the classroom doesn’t always have to come to a definite conclusion, and student’s don’t need to complete an activity if the discussion and journey are enough to help the students develop. If an activity is going to put strain on the student’s happiness, sometimes it is better to reconvene than try and force the students into completing an activity they cannot focus on, or is perhaps too difficult to accomplish. In an instance of extreme difficulty, a class can pause the activity, and the teacher can provide guidance to help the students in accomplishing the set task. As it was, our activity did not need an end, as we were merely testing  ourselves on our ability to remember and recognize the placement of numbers.

One of the other tasks assigned, the dot problem, also raised interesting comparisons to problem solving in the classroom. When we completed the problem, I had a different answer than the other people in the class, but it was also a correct answer. I had just gone about the question a different way. Problem solving allows for the circumstance of different outcomes and processes, as long as the integrity of the question is still intact, and the discovery at the end of the process remains the same. For example, a teacher could assign students to explore areas of objects and come up with ways to write out universal formulas for shapes. Students may use different variables or put *1/2 in comparison to ÷2, though both mean the same.

The final problem we worked on that I want to discuss is the handshake problem, because it brought about one of my favourite things about problem solving. When we were faced with the question, asking about the number of handshakes given, we never actually came to a conclusion. But we spent our time discussing the scenario and ways in which to figure out the problem, and positing different factors contributing to the question. The discussion flowed naturally and it was a way to enhance our ability and understanding even though we didn’t come to a conclusion at that time. With problem solving, allowing for free discussion and group work is an excellent tool. Students have the ability to learn from each other, as well as teach their other classmates, and gain a deeper understanding of a topic. As well, group work and discussion can be fun and engaging, putting a positive spin on to a math class.

In our class, we were taught about the critical factors in the problem solving approach being tasks that require the use of a specific method that is being taught, as well as tasks that inspire creativity and intrigue. The examples we worked on in our class were excellent examples of the creative thinking process as well as the questioning process. As a class, we worked on problems together, discussed solutions and had to stretch our minds in order to figure out some of the brain teasers. The application of the knowledge allowed us to see that critical thinking is the key to success and that problem solving allows students to be involved in the teaching process, not simply be taught at.