The most important Mathematical Porcess.

Processes in Mathematics include:

1.Problem Solving
2.Reasoning and Proving
3.Reflecting
4.Select Tools and computational strategies
5.Connecting
6.Representing
7.Communicating


After reading and watching ahead a bit (out of curiosity), I had my original ideas that communicating and reflecting were the most important processes. From an English teacher's perspective, these process are the most important because of the collaboration and possibilities for editing and proofreading. The process though I feel is important for students to acquire is "problem-solving", the process in which students need to acquire is one in which they are able to make mistakes and reconsider alternatives to it. In English, there is not as big a need for trial and error unless referring to the process of learning. In Math, the other processes are generally all equally important. I do believe though that the problem solving in the subject area of Math allows for students to develop and acquire the basis of all the processes listed (to an extent).

Rich Text Tasks

http://reasonandwonder.com/rich-math-tasks/

http://thelearningexchange.ca/videos/success-criteria-and-learning-goals-in-math-learning/

https://nrich.maths.org/6299

http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/CBS_AskingEffectiveQuestions.pdf

http://slideplayer.com/slide/5783059/

https://tapintoteenminds.com/4-part-math-lesson/

What is a 3-Part Lesson?

These are typically the parts of a 3 part lesson:

1. BEFORE – ACTIVATION, MINDS-ON The purpose of the first part of the lesson is to get the students cognitively prepared for the lesson problem by having them think about ideas and strategies that they have previously learned and used. The teacher might also ask students to solve a smaller problem in order to evoke prior knowledge and familiar skills and strategies. Through questioning, teachers seek to establish what students already know about the content and the context of the problem. Teachers listen for an indication of students’ level of readiness. Careful observation during this stage will allow teachers to pose further questions and prompts that provoke deeper thinking throughout the lesson. It is during the activation phase that students will recall previous learning and be prepared to apply it to the lesson problem and discussion. This is a good opportunity for students to ask questions of each other that are similar to those modelled by their teachers.  2. DURING – WORKING ON IT, ACTION During this part of the lesson, students are working on solving a problem and communicating and representing their mathematical thinking. This phase of the lesson provides multiple observational assessment opportunities, which may be captured as anecdotal or digital records. As students work to make sense of the mathematical ideas embedded in the problem, both teachers and students use questions to develop and clarify their mathematical thinking. Solving the problem during the planning phase helps teachers to anticipate some of the challenges that students may encounter and informs their questioning. By listening closely to students as they discuss their emerging solutions, teachers occasionally pose questions and use the information they glean to inform their in-the-moment instructional decisions. This information may also be used as assessment-for-learning data for planning purposes, including the planning of questions for lesson consolidation. Both correct and incorrect solutions can be probed, since questioning promotes the thinking necessary to build, construct and consolidate understanding.At times, however, questioning may not be appropriate, since the students need time to persevere through their thinking without interruption. 3. AFTER – CONSOLIDATION, HIGHLIGHTS AND SUMMARY, AND PRACTICE In this phase of the three-part lesson, the teacher strategically coordinates student sharing of their solutions to the lesson problem, using a mathematical instructional strategy like bansho, math congress or a gallery walk. During consolidation, teachers and students ask questions that help to summarize the mathematical ideas embedded in the class solutions. They support students in establishing explicit connections between solutions, concepts and strategies. As students analyze other students’ solutions, they question their own ideas and the ideas of others. They examine mathematical thinking, engage in metacognition and make generalizations related to the learning goal. By seeing other ways to solve the problem, they may adopt new strategies when they solve subsequent problems.

EDUgains materials for teachers

https://thelearningexchange.ca/projects/loving-the-math-living-the-math/?pcat=999&projectID=4601&prov=4601&sess=1

BIG IDEAS

Big ideas can:

• help you to cluster expectations
• create a more strategic, organized approach
• build stronger connections between strands/expectations/concepts
• deepen learning of fundamental concepts over time
• build fundamental concepts over grades
• simplify your teaching

http://thelearningexchange.ca/videos/marian-small-big-ideas/

http://thelearningexchange.ca/videos/instructional-big-ideas/ 

http://thelearningexchange.ca/videos/big-ideas-strategies-and-modelling/  

Engaging students in mathematical processes empowers them in math class. Mathematical processes support the acquisition and use of math knowledge and skills. 

What are the seven mathematical processes?

Review the following for a comprehensive understanding of Mathematical Processes:

• Capacity Building document entitled, "Yes I Can:Paying Attention to Well-Being in the Mathematics Classroom" (page 3, especially): http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/math-classroom2018.pdf
• Section on Mathematical Processes (pages 11 to 17) in the front of the Ontario Curriculum, Grades 1-8, Mathematics document: http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf
• EduGains provides a resource with sample questions that teachers can ask to develop the math processes. Look at the first two columns:  http://www.edugains.ca/resources/LearningMaterials/MathProcesses/MathProcesses_AfL-AaL.pdf 

Discussion Post: Which of the mathematical processes is the most important, in your opinion? Why?

How can we give the math process that you identified as the most important a high profile in student learning?

"I would describe a rich task as having a range of characteristics that together offer different opportunities to meet the different needs of learners at different times. What is also apparent to me is that much of what it takes to make a rich task 'rich' is the environment in which it is presented, which includes the support and questioning that is used by the teacher and the roles that learners are encouraged to adopt. That is, an environment in which learners are not passive recipients of knowledge, accepting what is given, but independent assertive constructors of their own understanding who challenge and reflect. On its own a rich task is not rich - it is only what is made of it that allows it to fulfil its potential. With this in mind it might still be useful to list some of the things I might say when describing a rich task. Rich tasks (or good problems):

• are accessible to a wide range of learners,
• might be set in contexts which draw the learner into the mathematics either because the starting point is intriguing or the mathematics that emerges is intriguing,
• are accessible and offer opportunities for initial success, challenging the learners to think for themselves,
• offer different levels of challenge, but at whatever the learner's level there is a real challenge involved and thus there is also the potential to extend those who need and demand more (low threshold - high ceiling tasks),
• allow for learners to pose their own problems,
• allow for different methods and different responses (different starting points, different middles and different ends),
• offer opportunities to identify elegant or efficient solutions,
• have the potential to broaden students' skills and/or deepen and broaden mathematical content knowledge,
• encourage creativity and imaginative application of knowledge.
• have the potential for revealing patterns or lead to generalisations or unexpected results,
• have the potential to reveal underlying principles or make connections between areas of mathematics,
• encourage collaboration and discussion,
• encourage learners to develop confidence and independence as well as to become critical thinkers."

 ~ Source: Article, Rich Tasks and Contexts by Jennifer Piggott - http://nrich.maths.org/5662 

Potential Resources Math Teachers Refer to in ON.

A teacher's guide

This guide is intended to support teachers' ongoing efforts in building students' knowledge and skills in mathematics. It focuses attention on the content of expectations in The Ontario Curriculum, Grades 1–8: Mathematics, 2005 that deal with fundamental mathematics concepts and skills (specifically, expectations in the Number Sense and Numeration strand and expectations that relate to number properties in the Patterning and Algebra strand). The guide outlines steps to achieving the knowledge and skills described in these expectations and suggests how to make more timely connections that will better support student learning. A strong foundation in the concepts and skills emphasized here will prepare students for success in high school, and ensure that they have a set of essential skills for employment and responsible citizenship in the future.

http://www.edu.gov.on.ca/eng/teachers/teachers-math-guide.html

A Parent's Guide to the Fundamentals of Math

Grades 1 to 8

Making sure that students have a strong understanding of the fundamentals of math is one of the best ways to prepare them for success, now and in the future. What students learn today will help best position them to solve everyday problems and to increase their employability in tomorrow's economy.

http://www.edu.gov.on.ca/eng/parents/parents-math-guide.html

http://www.edu.gov.on.ca/eng/curriculum/elementary/math18curr.pdf

Math ABQ 7/8 Activity 1 (M1)

I am completing an AQ course online with a university and will be posting my work up here to help me keep track and conduct further personal developments in my work and understandings of the course materials. Enjoy or comment for more information.

"Your First Post – Introduce Yourself: 

Introduce yourself:

    Tell us a bit about yourself.  Your introductory post may include, but is not limited to, the following:

• Your name and teaching assignment
• The length of time you have been teaching
• Why you are taking this course
• What you hope to learn/gain by the end of the course and any specific areas that you would like this course to address
• Your greatest success(es) in teaching math
• Your greatest challenge(s) in teaching math
• If you wish, your interests, activities, etc., within or outside of your work in education"

My name is Carmelo Bono, I have been teaching in China for a number of years (this is my fifth) and generally teach English, as well as a few other things. I do however expect that if I am able to continually improve my understandings of Math in the classroom, I can take my particular skill set and acquire a depth of understanding that will allow me to utilize it in the classroom. In teaching Math, my greatest success so far was a lesson in teaching probabilities, mean, median and mode. It was excellent because I had all the students participating in a class activity using tokens they enjoyed talking about as they worked; they also found the activity entertaining as it was set up for them that when they came in from recess they were instructed to reach beneath their seats (as the resources were taped there) and acquire their tokens for the game. Students had a lot of fun and although there was some set up, it was worth it.

I feel that my interests are in innovation and overcoming challenges (personal and professional). It seems to me that with the way teachers are able to adapt society, and technology into the classroom that there are many opportunities for teachers to create quality learning moments in Math because it is a very functional and tangible idea in everyday life.

Teacher Leadership Pt.1: M1_FA 6B)-HOD Position Concerns and Commitments

I made this post long ago-I'm guessing it was going to be about how silly and backwards "Maple Leaf Education Systems" is. I honestly, have vented so much about that god forsaken wasteland, that-whatever. I digress, 

Let's first talk about the purpose of this post is, "I'm new to leadership-what do I do?"

Next, let's define some of the terms we will discuss,

HOD's (Head of Department)-British Columbia Jargon

DH (Department Head)-The rest of the world's understanding of the term

To sum up, in the event you are reading and aren't interested in rants, "its an impossible task list basically, and at the end of the semester-as long as no one throws a temper-tantrum or quits, you have succeeded in the position. If you can build up staff morale, your not getting paid enough."

 
Revisiting this at an opportune time to spruce it up with connection to my current enrollment into Teacher Leadership pt.1 AQ,

As per module 1 and focus area 6B),

"What are some challenges of being a leader? Provide a summary of what a challenge may look like, sound like and feel like.

Review and comment on two other postings by your colleagues."

As per discussion, 

"A department head or in a position of leadership, ALWAYS (in my honest opinion), in regard to challenge-morale. Staff morale changes like the wind. Yes, GENERALLY there is a happy staff or "good" work environment. People are humans, cats are cats, and dogs, well are dogs, the point is, people get hungry, people get thirsty and are allowed to feel "burnt out", "tired", "restless" or like they are having "a bad day". That's normal and that is the hardest part about being a leader. 

Leaders are people who are often solving/preventing a lot of issues with the help of others (heaven forbid, by themselves), but still need to find time to be human. I'm not trying to say being human is hard, but it is similar to the idea of how a lot of us need to sometimes bring work home (or work from home) with us when our kid(s) are at home and want to "play" or "make popcorn" and you are saying, "one moment, yes I'll get to you in a moment-almost done". I'm not proud to say that I have been in that position before but that's a fairly accurate analogy in which we overlook the "human" aspect of our job (especially as a leader). How many times has a leader ever said to you, "let me get back to you on that," and (spoiler alert), they don't. In some business offices, ya sure, I can see this is a way of getting people who have silly "issues" to learn to deal with it themselves (I can say I wholeheartedly agree, but I get the perspective a busy manager may have when say 10 let alone 100 people email your IT department for a tech error). However in the education field (let alone as a government employee-however many times removed), that is just unacceptable-pretty sure that is a grievance :/ sorry-I digress, but the fact in the matter is, leaders are humans, but we sometimes need to remind ourselves of that. 

At least, that's my challenge. Stopping-like now, see ya later. "

How to Keep Confident as a Teacher

A few easy ways to keep your confidence up as a teacher who is new to the position.

1. Dress the Part- You are not dressing up as a good as say a mob boss, but you can still look good, at the very least a tie and black polish-able shoes. Remember, comfort is crucial! As for pants, go for dress-however in smaller schools it is not uncommon to see coloured "denims"-for ladies, you are well expected not to show off breasts, cleavage, toes, or bellies. With that in mind yoga pants may be common in some working environments-for your own personal image it is highly recommended to avoid where them as a teacher.

Really for young professionals it is generally the same in most places. If you don't feel comfortable wearing it-you probably shouldn't be (even if it does look right, it will mess up your vibe for the entire day). Invest something that looks nice and feels good.

  

2. Be prepared for class-  It is not unheard that a teacher leaves something important in their office and needs to run back to claim it. It is also true that different working environments have different norms due to the fact that understandably people make mistakes when "multi-tasking" (not a thing by the way). It is important that teachers remember to bring everything needed to the office, classroom etc. however some teachers are constantly moving copious amounts of things from "A" to "B". This means that there is a higher possibility of leaving "something" behind. 

TIP: Take what you need, avoid carrying extra stuff between class and office.

Investment Opportunity: Laptop bag or professional looking school bag.

3. Genuine Listening Skills- As a new teacher you SURELY had "genuine listener" on your resume and cover letter as a marketable skill! If not, you certainly should consider it. But aside from having that skill written down-make sure you "got it down". Listen more than you speak. Take advice, ask questions-don't demand you are right because in reality-you just arrived. More to see than do at this point in your career.

4. Keep it Simple at First- I'll be honest this is the hardest one for me. Choose your volunteered tasks wisely and set goals. Know what you want out of this first experience and then create a plan of how you are going to grow. My first year yielded a marking time till about  9 PM most nights and I would be the first one in the office (sometimes even the school at 6 AM). It worked out, but I certainly felt the relief of difference when I finally got to vacation.

5. Pay Attention to Your Success- Don't get bogged down by a mistake, learn from it and feel proud of what you do well. For every mistake you make, someone else will also make one. You may feel like "I was the last one to mess up and no one will ever forget" until someone else does make a mistake.Not the best way to look at it but in reality the way the human brain works, usually that is how people feel. The best thing to do is reflect on your possible opportunities for improvement in the future. Don't go and frame or create a situation for anyone (making enemies and "framing" are forms of workplace bullying and possibly even discrimination-don't engage in conflicting personalities). 

6. Seek Support From Your Colleagues- Help is good, it doesn't make you inferior. You are teacher for goodness sake. Is this not what we tell the students?

7. Set Professional Goals for Yourself- 21 Days of Teacher fashion on social media; 21 days of home made lunches; 21 days of different books read-these may seem like goals and sure to extent they say something about your character. A professional goal should look something along the lines of long term. If you are not that far into your life where you are thinking that you are interested in promotional opportunities in the near future, start off small. Delivery of timely feedback, saying hello to most people that pass you in the hallways, etc.

8. Stay Organized-This is most certainly the hardest for me. Hands down though it makes a difference, especially when you need to role model.

9. Control- Even in the most chaotic of times, you need to remember you are the one who is in charge of roughly 30 people at any given time. Do not snap, lose your cool or break. When you feel a meltdown coming on. Sometimes it is a good time to have an energizing moment with your class or plan some more relaxed activities for the class rather than content heavy materials.

10. See Opportunities Instead of Disasters- As mentioned earlier before, stay positive and look at what you do well; reflecting on failures for the sake of self-improvement is important, but don't dwell on mistakes.