My Journey from a High School Math Student to a Teacher...

I am in grade 7 - math is always interesting and it does not let me realize the time that I spend in solving all these questions every day. I keep on working, sometimes I have to redo, but I never give up. I am good at memorizing tables and formulas and also using them during problem-solving. I am doing great, scoring almost 100% in every test and exam.

Now, I am a high school grade 11 student and all of a sudden, math becomes extraordinarily difficult, nothing is making sense to me. What happened? What am I doing wrong? Why am I not excelling and thrilled about math anymore? The teacher comes in the class, fills the blackboard with white chalk and goes on. Math is still my favorite subject but I don’t seem to be interested anymore. Realization -memorization is not working anymore because math concepts are deeper and complex. I need to understand math not to just solve a problem.

A huge transition, learning to teach high school math, and this is when my journey from memorizing to conceptualizing mathematics starts. There are new pedagogical strategies, for example teaching math through inquiry and three-act math etc. It’s a whole new world to me because as a student I have only seen lectures in high school math class. Assessments are not just shaped as quizzes, tests, and exams anymore but there are so many other differentiated assessment strategies for example rubrics, checklists, peer-assessment, and entrance/exit slips that can be used instead of traditional assessment methods like tests, quizzes, and exams.

My Survey results from high school math teachers:  A rural high school math teacher says, “Inquiry at the high levels of math doesn’t work in my opinion and if it does, then it takes too much time. It is possible to use inquiry with Work Place & Apprenticeship because there is more time and content driven project opportunity but not with Foundations and Pre-Calculus. Also, split curricula confront practicing adaptations.” The teacher uses a mixture of tests, assignments, and differentiated assessment strategies to assess students. On a Native Reserve, the high school math teacher faces different challenges in his teaching, for example, irregular attendance, less cognitive abilities, underprivileged living to mention a few, that can affect a student’s learning.

During all of these transitions, I felt that a change is required in teaching and assessing math in high school. I agree that there are some circumstances where we do not have the choice to incorporate different pedagogical and assessment strategies and current practices are harder to challenge. But still, we can at least try to adapt them. Then critical analysis of results from these adaptations will guide us to the next plan of action. Students are diverse. The curriculum math streams are also different in nature from each other. Therefore, I think we can not generalize in regards to teaching and assessing math but as teachers, we should always be critically noticing our students’ potential and flexibility to meet the change if/when introduced. These critical observations will provide a great insight as to what practices can be successful with these students. Since we also learn from our students we must always refine our pedagogical and assessment strategies. It is a journey where we can continue to get better as we observe and learn.

In conclusion, I would like to share a great resource Reflections of a High School Math Teacher with readers of my post. Dave Sladkey is a high school math teacher who loves his job and likes to learn new things to become a better teacher. The blog devices a great learning opportunity especially for future educators.

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Inquiry-based teaching and learning - Entry # 4

1) What/how are you learning about inquiry in this course (through your readings, our class activities, lesson planning and teaching)

The other day, I was reading an article on ESCHOOL NEWS which was more related to ‘technology in education’ but before I read through the article I was stunned for some moments just by seeing the title ‘if you can google it, why teach it’. I started to think about the role of a teacher in today’s classroom which has become more challenging in the world of Google and technology. I experienced the same tension while reading the article on ‘teacher change’ as Brea stated in her story of transformation: who I was, what did it mean to teach, what is my place in the social and cultural world in which I and the students live, how could they then become something otherwise?

This is how I started to recap my own teaching experience, what I have been learning about inquiry throughout my EMath course, and how can I bring a foundational change in my teaching practice from lecture-based to inquiry-based by following a process of self-understanding, self-construction of knowledge and experimenting with possibilities. Here is a short snapshot of my notes:

• Inquiry-based learning is more about triggering curiosity than just asking a student what he or she wants to know.
• Mathematics is a living discipline and the curiosity of the students plays a key role in guiding the flow of the lesson; teachers need to be more prepared than planned.
• Teaching mathematics is not only a job of teaching but to challenge students intellectually and engaging them with the mathematics. It is to let them make connections between math and real-world.
• In an inquiry-based lesson, answers would be uncertain; the work would constantly be unfinished but the openness of topics may lead students to think (they might not usually think in every situation). ‘Thinking’ might bring innovation which can lead towards improved understanding.
• The topics in math class won’t be set and flattened but as teachers encourage inquiry, the students develop their own skills as content-area experts.
• It transfers some responsibilities from teachers to students, and it’s good because releasing authority engages students. And a common belief is that learning improves when students are inquisitive, interested, or inspired.

Inquiry-based learning

2) How/if the ideas in the article challenge or affirm your beliefs about mathematics teaching & learning.

I agree with the ideas presented in the article and these are my reasons:

1. Math is a living discipline; love is a part of living discipline; thus, it affirms my belief that math is a subject of affection and love.
2. We should begin to give voice to, or recognize the voice of, students, thus empowering them. Empowerment would enable students to bring innovation, creativity, and diversity in learning math and solving problems.
3. As Joseph Joubert said “To teach is to learn twice” and this article affirms that Inquiry-based teaching is a process of continuous learning and growing experience.
4. Through inquiry-based learning, students contribute to the field of mathematics and they start to understand that they have a role in it. I think one’s role and contribution triggers or provide a basis for new inventions of the world.

How do I grade – Assessing student learning

There are tons of assessment strategies that can be used in the classroom for formative and summative assessment but I will talk more about “Rubrics”.

To be honest, I hadn’t heard about rubrics as an assessment strategy before taking the courses at the U of R. But I have a pretty good understanding of it now after researching and reading about it. The main purpose of rubrics is to assess performances. There are two main components of rubrics: criteria and descriptions of levels of performance. Rubrics is an important tool, because they clarify for students the qualities their work should have.

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Following are some of the advantages and disadvantages that appealed to me the most:

Advantages:

·        Improved students’ self-regulatory skills

·        A consistent assessment

·        Math is conceptual (explaining reasoning)

·        Partial credit for work (marks for procedure)

Disadvantages:

• Limit imagination and innovation
• Takes time to develop, test, evaluate, and update
• Unsuitable for some younger children as comprehending multiple strands can be challenging.

During group discussion in class, I also heard very good opinions about “Portfolio” and “Checklists” along with some other assessment tools.

  

The purpose of a portfolio is to showcase students’ progress over the course of a session. They are able to identify their strengths and weaknesses through self-evaluation. Some of the main goals of portfolios are to see "student thinking, student's growth over time, mathematical connections, student views of themselves as mathematicians, and the problem-solving process. ERIC

Checklists can be used for formative (ongoing) assessment to monitor students’ behavior and progress towards reaching stated goals. Checklist is a better tool to record teacher’s observation during routine classroom activities.

Value of performance-based assessment in relation to curriculum and instruction:

These performance-based assessments are the best way to assess students consistently and to align the intended learning outcomes with curriculum. Assessments are often designed in terms of students understanding the learning target and criteria for success. For this reason, they help teachers teach, to coordinate instruction and assessment, and to also help students learn. To select and design any assessment strategy, teachers have to focus on the criteria by which learning will be assessed. This focus on what they want students to learn rather than what they intend to teach helps improve instructions. I am really looking forward to using some of these assessment tools in my future classroom. 

Significance of teacher's beliefs in teaching & My mathematics creeds - Entry # 2

I pretty much agree with the research and analysis presented in the articles (Kim Beswick & Merrilyn Goos) regarding mathematics beliefs, knowing and doing mathematics and its importance as a subject and as a tool.

What we believe about the subject as a teacher influence our teaching style and I think this then makes (or affects) student’s vision or belief about the subject. Teachers are the first ones who introduce the subject to the students and they are the main source for them to start believing what is this subject, how difficult or easy it is for them, do they like it or not. Hence, I would say teachers should be very cautious in their beliefs, words and actions about mathematics as it is going to reflect in their students which can last, sometimes, forever with their lives and we would be responsible for students’ love or hate for the subject.

Knowing and doing mathematics is not different than knowing something else in the real world (knowledge) and then to know where would it be applied when it comes to its application. Knowledge and understanding about something are two interconnected but different things. If we know something with understanding, that’s where we are in the position to reflect/transfer it. So being a main source for student’s perception about mathematics, teachers should demonstrate mathematics as a part of real world.

Mathematics is important to learn as it is just not a subject but a tool and a tool kit is not complete with a missing tool. It is about connecting ideas and sense-making. For me, it is also an enjoyment and a source of happiness by giving a sense of accomplishment.

My Mathematics Creeds

1. I believe that mathematics is not just a subject to learn and teach but it’s an affection and love. This passion about mathematics can make someone enthusiastic about it and it will lead towards making sound grounds of it.
2. I believe that learning mathematics is not just beautiful and pleasurable but also interesting to solve problems in the practical life. It helps to bring innovations, creativity and diversity in real life problems.
3. I believe that learning and teaching experience of this subject affects very much on one’s career selection and if we have good mathematics learning memories then most probably we will choose a career of educating this subject and by the quote “teaching is learning twice” we will be on a journey of always learning new things.
4. I believe that I feel enjoyment while teaching geometry in mathematics because drawing triangles, circles and rectangles using compass and scale is like doing an art work while solving the problems.
5. I believe that mathematics is one of the key subjects of all the inventions of the world starting from simple calculator to complex and super computers to huge buildings, bridges and even tabulating the results of medical experiments/researches and much more. I also believe if it was not mathematics then human might still be living in caves. 

"Blog About it" Entry # 1 - Mathematics Autobiography

“Mathematics is one of my favourite subjects”, it is not just a repeatedly used common sentence for me and its not just a sentence about liking a subject, I have a deep relationship and a connection with mathematics. The reason of this relationship is not that I used to be very good at doing mathematics but it was an inspiration to it. I was born in a house where mathematics used to be everywhere, my father was a mathematics teacher and he used to teach it in a school as well as at home (home tuitions), I saw him making a strong base of it first and then constructing a building on top of that passionately. It was very interesting to see how things are interconnected with each other and how mathematics building grows gradually as we go in advance studies.

My journey to mathematics began at a very early stage, I started to learn and teach mathematics at the same time, me and my sister were class fellows from Kindergarten to Grade 12 and I used to teach her mathematics, moreover, my father always encouraged me to teach his students at home. This is how I got inspired by this interesting subject and learning it had become an enjoyment by practicing it through teaching.

I believe mathematics is a subject that helps nourish the mind. It gives opportunity to think from different angles and gives freeness to make your own way to get to the solution. This subject is diverse and as we know diversity makes the life beautiful. I feel inner satisfaction and happiness when I get to the solution of a problem by solving it in a way I want and it would motivate me to do more and would never get tired of it.

In my opinion, mathematics is not just a school subject to learn and pass the exam, in fact, it helps us in our day to day personal and professional lives. Skills that we learn from mathematics may be applicable down the road like in learning other subjects, in our jobs and to excel better in other fields as these are transferable skills. Mathematics skills give us ability to identify and analyze things, to see the relationships and to solve a problem by thinking logically as well as critically.