# The Final Countdown (see what I did there, it’s a math pun)

EMTH 200 has been really helpful in emphasizing the importance of teaching mathematics through problem solving.  It has helped to teach me that when students figure things out on their own, they are so much better at remembering and applying their learning, no matter the subject area, but especially in math.

There are many ways that a teacher can use problem solving to teach their students.  They can use Guess and Check methods, in which students use critical thinking to guess the approximate values of things, check the answer, and then modify their approach if they need to.  Students can Make a Model, in which they create some sort of graph, diagram, or picture to help themselves visualize the problem they are trying to solve.  Students can try to identify Patterns, or they can use Elimination or a Table to reason their answer out.  There are many things that students can do to find the answers to their given math problems, which is why it is such an effective tool, because students are able to use whatever method they find most comfortable to solve the mathematical problems that they face.  That is why it is so amazing.

What I have learned in this class is that it is okay for students to struggle.  Without struggle students are unable to take hold of learning and make it their own.  Without struggle students are merely receptors of information, and not actors upon the school curriculum.  It is also important for students to have the opportunity to collaborate.  Humans are social creatures, and as such we are much more productive when we work together.  Ideas very rarely pop out of just one mind, but instead advancement is made by building upon the work of others, and so students should have that same opportunity to collaborate with their peers to most thoroughly and completely solve the given problems.  I have also learned that understanding takes time.  People do not immediately understand things, and when solving problems may need to take a break and come back to the problem with a clear and refreshed mind, so again, students should have the same opportunity.  The benefit of having classes everyday in school is that if a teacher has a difficult problem that students need to solve, and gives them a little bit of time each day to try to solve it, with patience and guidance students should be able to solve the problem.  One final thing I think that I will take from this class is to encourage failure among my students, because failure should not mean that the students fail, instead failure should be taken as a learning opportunity.  It is the trying, failing, and modifying process by which the world works, so why should it not work the same in classrooms?  When students feel free to fail, they will be much more willing to try, which is exactly what teachers should want their students to do.

Problem solving is an incredible tool for teachers, and as a teacher I intend to use it.

# We must Assess the damage done here

Today we talked about assessment, thought definitely not for the last time.  You see, assessment can be a very controversial topic, because it can be done in many different ways.  Traditionally, assessment has been completed by using assignments and tests to see if students know the content, but that is not an effective way to reach a lot of students, and so teachers should assess in many ways at once to get a more rounded picture of the student`s understanding.  Another topic that has been coming up recently is the idea of twice-done assignments (I`m totally coining that term; it`s mine), and how a good way to encourage student learning is to not keep assessments like homework assignments as final grades, but instead do some editing and allow the student to try again to hand it in again.  I know that would work well for other classes (especially those that include large written assignments), but I`m not sure how that would work for math.  Either way, I am continuing to believe that when students are presented with assignments that determine final grades, then they do not do the best that they can, but when a teacher is willing to help them through their mistakes, they are more willing to make them and subsequently learn.  Tests are final, I get that.  They are summative assessments of what the student learned throughout a unit or class, but formative assignments should be for encouraging learning.  Even if all the teacher does is grade it, give it back to the student, allow them to hand it in again, grade it again, and then take the average between the two marks, it would show what the student knows, it would encourage the student to try on both assignments, it would teach the student what exactly they were having difficulty with and encourage them to examine and correct their own mistakes, and it would not penalize students for not knowing everything right away.  I see this example as a fairly simple procedure to implement, even if it does add a bit more work to the teacher (grading it twice), but I think the benefits are incredible.

So, I still do not know a lot about assessment, but I am learning, and I want to be a teacher who is always learning so that the classroom in my last year will be better than the classroom in my first year, if only because of new ideas.

What do you guys think?  Should assessment be the same as it always has, or should it be changed?  How much should it be changed?  Is this the best way to teach our students?  Like I said, I don`t know everything, but I do know that I want to best for my students, and so I will continue to learn with that end goal in mind.

# Making the Lesson Plan

Last Wednesday we continued to work on possible activities to teach certain lessons.  My partner and I came up with some pretty good activities to help teach comparing and pricing skills, as well as puzzle solving skills.  For the comparing and pricing, we thought that it would be good for students to actually go to grocery and bulk food stores to compare prices on specific items, that way they would learn how to actually see which is cheaper, and if it is more practical to purchase items in bulk rather than just buying what you need.  For solving puzzles, we came up with the idea in which students would be given specific items and a crate, and then be asked to organize those items in such a way that they would fit within the crate unobtrusively.  With each activity we also came up with differentiation strategies.  After this we began to actually work on lesson plans, and it has been very helpful going through all the processes.

I have learned a lot just through working through the lesson planning process.  After deciding on a topic, one then needs to come up with how the lesson will actually accomplish that goal.  It is difficult trying to come up with activities and good teaching practices that would work for students, and it is especially difficult not to resort to lecture style teaching that, while being much more easy to plan and implement, produces very little in the way of actual learning.  For the lesson plan I was hoping to achieve, students would learn about area and how to best divide up land for a given number of people, while also taking into consideration that everyone needs to have easy access to the water.  I would use this activity to test the mathematical skills of the students, but then would be able to cross over into a social studies lesson in which I would be able to talk about the Metis river lot system, in which the Metis divided the land into strips so that each land owner, specifically cattle ranchers, would have personal access to the river.

I do not know, but I thought it was at least an interesting idea.  But like I said, going through lesson planning is teaching me a lot, and I am coming to realize that the only real limits are the ones that teachers put on themselves (well and maybe financial, or time, or a number of other things, but I have not reached those yet).  And so, education continues to teach me how different the profession of teaching is from other professions.  Oh well, at least it won`t be boring.

What are your thoughts, do you have and lesson planning ideas? What other sorts of cross-curricular connections come to the top of your head?

# Engaging Students

Lately in EMTH we have been learning that engagement is the key to Problem Solving and to learning in general.  People learn much, much better when they are engaged with the content that is being presented; and, when if a student is Problem Solving, they are much more likely to push through difficulties in pursuit of the answer.

When creating a Lesson Plan, a teacher must have a good Set, that opening in which students are given a glimpse of what will be learned and are drawn in.  Throughout the lesson, a teacher can encourage students to solve problems by asking focused questions.  Questioning to a specific direction is key pushing students through barriers they might face in the pursuit of solving a problem.  Other ways to engage students is to set real life tasks, things that the students know are applicable to their lives, and to build on what the students already know.  Whatever the teacher does, he/she must engage the students.

Engaged students are students who are open to learning.  So, creating an engaging environment provides an essential catalyst in the pursuit of knowledge, understanding, and overall learning.

# Planning a Math Lesson

Hey guys, sorry this post is a little later than usual, it’s been a pretty week.

Ok, here we go.

Last Wednesday we talked more about Problem Solving (shocker) and how it should be promoted through an inquiry approach.  Teachers must encourage students to learn by initially intriguing them and then leading them through fascinated discovery.  Learning needs to be student centered in which students are actively engaged with the content, the teacher, and the classroom to help build understanding.  The goal of teaching should be to inspire learning, and students learn best when they are interested in the content.

To lead to inspirational learning, teachers need to plan out the lessons well.  One good way to do this is to use the backward design approach, in which teachers first start with what they want the students to learn (outcomes and indicators) and then work backwards, finding how they will get from what they want to learn to what they already know.  Teachers can develop tasks for students to complete that help to encourage a pursuit of the knowledge the teacher is presenting.

Without inspired learning, school becomes at best a necessary place to get facts and earn grades in the pursuit of higher education, and at worst a terrible drudgery through which all must wade if they wish to continue education in any capacity.

# Mathematics as Sense Making

Today in EMTH we learned about Sense Making, or how a teacher knows when a student is making sense of what is being taught and how to encourage it.

We started by working on an activity that we had been eyeing at over the past few classes.  It had to do with hand shaking, and what I understood from the question was, that if a party was only attended by couples and some people shook hands, how was it possible for everyone to have shaken a different number of hands?

So, my partner and I began to work on it.  Firstly, because of the vague question, we established a couple of assumptions, such as a person may not shake hands with him/herself, and we also tentatively added that a person likely won’t shake hands with his/her spouse.  As a class we had also decided to begin with a party of 10 people, to more easily find some answer after which we might move backwards towards an unknown number of people.  We created a graph to find that with these stipulations, it was not possible for everyone in the group to have shaken a different number of hands (ex. for a group of 10 people to shake a different number of hands then one must use the numbers 0-9 considering that one cannot also shake their own hand, but it is not both possible for one to shake everyone else’s hand [9] and for one to shake no ones [0]).  After that we removed the assumptions to create a possible answer, but decided that there should be something better (it might be awkward for one to try shaking his/her own hand).  It was then that I realized that we had assumed a stipulation without writing it: each person was only shaking another person’s hand once.  Well, after that my partner and I were able to create possible scenarios in which both the original criteria (don’t shake own or spouse’s hands) were met, and everyone shook a different number of hands in total.

The activity showed more than anything that students come in with presuppositions, and so when a teacher tries to teach something more figurative or abstract, then a student might have difficulty wrapping their head around the foreign concept.  So, for a student to be able to make sense of a topic, one thing a teacher might do is put it in more familiar terms, like using a real life example.  When math remains abstract, not only is it difficult for many people to understand it, but because of their lack of understanding it becomes increasingly irrelevant to their lives, and then what is the point of teaching math if students are not going to use it?  There will always be some math that is not applicable to the everyday lives of a lot of students, but when a teacher explains math in a way that students understand, they will be able to apply it to their lives more, and maybe even increase their overall capacity for understanding.

That is the kind of teacher that I want to be.

# How does one teach Problem Solving?

Today was a bit different, but very practical and necessary for our learning as teachers.

Today we learned about the Saskatchewan Curriculum Guide, naturally focusing on mathematics, as well as how to use it to then formulate class lesson plans.  We have also been talking about it in our ECS 300 class, which I have found really emphasizes how important this guide is.  The reason it is so important is that it contains the curriculum for every class that can be taught within the province of Saskatchewan, and more importantly the outcomes within each curriculum.  An outcome is a provincially set goal that all teachers across the province are expected to teach their students.  With the outcomes come indicators, which are suggested ways in which a teacher might teach said outcomes.  I have found this learning absolutely indispensable, as this is what we as teachers are being paid to do.  This is the core of our jobs.

With these outcomes and indicators, we have been taught to create lesson plans.  A lesson plan is literally that: the plan of a lesson.  In each lesson plan there is a basic structure.  Firstly, one must define what he/she intends to teach, what outcome that fits in with, and what indicators he/she will use to know it is being taught.  Secondly, one must be able to bridge what has been previously taught to what will be taught, to give context for the lesson plan.  The teacher must then develop a pre-assessment, some sort of device to test where the students are at.  After this, there must be the lesson plan itself, with the hook or set to introduce the topic, the development in which the teacher elaborates on the topic and teaches the content, and then the conclusion in which the lesson is completed.  Interspersed in this must be designated activities for both the teacher and the learner (i.e. complete a worksheet) and approximate time limits to keep the lesson on schedule.  After this, the teacher must have a post-assessment to see if the students learned what was just taught.  A good finish always has a summary of the lesson; it allows the students something short to wrap up their learning and remember the key points of what was being taught.  After the lesson is completed the teacher then needs to see what worked and what did not, so that the next lesson will be better than the last.  Not all lesson plans look exactly like this, but they follow the same basic structure.  Other things a teacher might add to the list are classroom management strategies for if students are becoming distracting or things of the like, or what resources will be used and how each one might help specific learning styles (eg. using a YouTube video, which both breaks up the lecture and stimulates visual learning).

This seems lengthy, but it is organized, and it allows new teachers a place to begin in their teaching, as well as getting them familiar with the curriculum.  Overall, I like it, though my response might be different once I actually attempt to write one.

Have a great day!