Blog Post #5

Throughout my field experience I used multiple assessment strategies both formative and summative. The summative assessment consisted of a unit exam, a quiz, poster project and hand in assignments. These were all executed after multiple formative assessment to make sure they are understanding the concepts in mathematics. Normally, I wouldn’t include the quiz as a summative assessment because this was my way of checking for understanding not for a mark, however, that wasn’t the case. Also, if students didn’t do well on the quiz I provided another opportunity to write the quiz. This was an opportunity that may students were grateful for and improve greatly after working with the concepts more. My formative assessments consisted of exit slips(sticky notes), homework checks, peer and self evaluation, checking for understanding through thumbs up/down/sideways, Plickers ( technological tool of multiple choice questions), Cartesian Plane battle ship game and stations. All of these provided the opportunity for me to check for understanding on all topics whether it be before, during or after a lesson to prepare for the next day and topic. We began our three week block with reviewing the aspects of the Cartesian Plane in order to move into graphing. At the end of the class we asked students to solve a problem involving linear relations and put their work on a sticky note which they would put on the board.  Whenever the class was not engaged I would do I quick assessment of are we understanding by having students close their eyes and give me a thumbs up/down/sideways. Plickers was a great assessment tool for students to engage in. Students would hold up an answer for a multiple choice question and I would scan the room with my phone and all  the students answers would be saved to my account. The list was endless and constantly assessing allowed me to reflect and plan lessons that would benefit my students. As a student I understand and know that it is extremely frustrating being assessed on something that is freshly taught, therefore, this helped me with my own teaching practice.

My pedagogical strategies that I relied on in my field experience was guided inquiry, activity based learning and direct instruction.  We did an activity where students tied knots in ropes and create a graph representing their data. This lead to a great discussion about whether or not we connect the dots or not.  When we discussed what the line would represent and this lead to a “grey” area of math. Students suggested that if we didn’t have the same size knots then would could get a value in-between points but this would create the dots to be closer together. This inquiry approach lead to a lot of “aha” moments. Our grade 10 class consisted of mostly direct instruction, however, the students benefited the most from an activity based approach. This approach allowed students the opportunity to experience their learning. In the future, I hope to have a happy balance of inquiry, activity based and direct instruction.

Blog Post #4

Over the course of this class and previous years I have been introduced to the process of learning through inquiry. At the beginning, it was tough because it was challenging my previous beliefs our how students should learn mathematics but as time went on I understand the importance it has in students learning. Inquiry tells us a lot about who are learner are and how they approach problems when we aren’t there to guide them through every step.  I have learned that students discovering their learning through inquiry allows them to connect to the content and they are able to create a deeper understanding of the material that they take further in their lives. I have gathered that inquiry is a learning strategy to increase student involvement, understanding and connections in mathematics and the world.

Something that registered with me while reading the article was how Brea stated:

“Since starting to engage in the inquiry kind of work that we are doing in my classroom, mathematics has become beautiful again. I want my students to understand that mathematics is not simple, that it is complex and complicated…” (Chapman, O. & Heater, B., p.450)

because it related strongly to my creed. Inquiry brings the purpose back into mathematics and creates an experience rather than just teacher for regurgitation. It is not good enough to simply teach in a classroom but instead create deeper understanding and use students ways of learner to do so.

 

Reference:

Chapman, O., & Heater, B. (2010). Understanding change through a high school mathematics teacher’s journey to inquiry-based teaching. Journal of Mathematics Teacher Education, 13(6), 445-458. doi:10.1007/s10857-010-9164-6

Blog Post #3: Forms of Assessment

Assessment is a continuous process and takes various different forms and levels of complexity. For instance, the assessment strategy I researched, checklists, was a quick way to assess through monitoring students behaviours and specific skills. Checklists are important in students learning because they keep students on track, easy to use, show that we value students learning on a daily basis and so much more. One of the biggest messages I took from the sharing activity was how much all assessment tools can work off each other and be woven together to better the learning of your students. For instance, reflective prompts, self assessment, checklists and journals can all be used in unison to create a portfolio, where students can see their learning progress and reflect on what happened at the beginning of the year to the present.

I am fascinated by portfolio’s and all the have to offer in mathematics. I would have never saw the benefits of a portfolio in math until today. They give student the opportunity to see their learning goals and constantly reflect on their learning instead of the “one and done” or “remembering math until after the test”  attitude in learning mathematics. Portfolio’s also allow teachers to see what students are struggling with, what their strengths are and their thinking process is when solving problems. For instance, in a lesson we are planning for Foundations 10, we are using a portfolio throughout the unit for students to keep track of their work which will benefit them in the end where they do a summative project, putting all their learning in action. Another assessment tool I enjoyed learning about was journals. I think that this can be very beneficial in mathematics but is often seen as the place it shouldn’t exist in. That mentality is utterly incorrect, because journal can often tell us what they aren’t or are understanding, their thinking process and allows them to reflect on their ideas and possibly challenge their ways of thinking.

“Our assessment tools must capture all of these aspects of student thinking to be effective” ( Mathematics Assessment: A Practical Handbook, p. 11). Assessment is a crucial  stepping block towards a successful learning environment. Without assessment as, of and for learning we can’t take the necessary actions to improve our students individual learning. Without assessment, our instruction does have a learning goal therefore what are we setting our students up for? Failure. Though various assessment strategies teachers can set their students up for success, while meeting the needs of a differentiated classroom.

National Council of Teachers of Mathematics (1999). Mathematics Assessment: A Practical Handbook for Grades 9-12. Reston, Va: NCTM

Blog Entry #2: Teachers’ Mathematical Beliefs

The Stereotypical Mathematics Teacher.

Screen Shot 2017-01-16 at 10.35.06 AM.png

Photo Credit: Teaching Secondary Mathematics by Merrilyn Goos, Gloria Stallman and Colleen Vale

Our mathematical beliefs influence our way of teaching daily; and these beliefs can change with new experiences and new ideas being developed but our core values and beliefs often stay the same; our students aren’t the only ones learning and developing their identity. Our beliefs are important because they shape who we are as teachers and how we execute knowledge in a classroom. There is an interconnectedness of beliefs, experiences and practice when teaching mathematics. When I first entered the education program, I would have taught mathematics exactly how I was taught, through traditional repetition and memorization because these ideas greatly developed my learning identity through high school. However, by developing my teaching identity and being introduced to inquiry and learning through discovery my mathematical beliefs have shifted towards a more beneficial way of learning. This is a huge knowledge factors for what it means to know and do mathematics. A shift towards a new way of learning is being made to better students’ understanding not simply computing information for tests. Mathematics is important to learn in an understanding manner because it continually effects the mathematical learning for students farther than a high school education.

Raymond’s model of the relationships between teachers’ mathematical beliefs and their teaching practice:

Screen Shot 2017-01-16 at 10.35.17 AM.png

Photo Credit: Teaching Secondary Mathematics by Merrilyn Goos, Gloria Stallman and Colleen Vale

I Believe…..

  • A positive mathematical experience in the classroom leads to a positive reflection for students. Many factors can effect a students experience whether that be the teacher, peers or parents. A negative attitude can often be related back to a negative experience.
  • If mathematics is taught with excitement and inquiry students don’t only gain content but an experience as well; which will stay with them a lot longer than memorizing a formula.
  • Mathematics and the teacher  should have a purpose. Without a purpose mathematics has no end goal and as a teacher if you don’t have a purpose for each lesson or day, then there are no expectations for students and your classroom.
  • Mathematical learners can have various ways of getting to the same end point.
  • That simply teaching mathematics is not enough in the classroom; a teacher must consider student relationships, types of learning, safe environment, etc.. A positive classroom and community environment can effect students learning drastically.

Blog Entry #1: Mathematics Autobiography

Screen Shot 2017-01-11 at 11.17.11 AM.png

Photo Credit: via Google

Mathematics has been a long road of ups and downs. Most of the ups came in high school where I excelled in mathematics and teachers didn’t have to worry about me paying attention or understanding the material. Math in high school was as simple as showing up, doing an assignment and writing the exam, never having homework or the need to study. However, in university everything changed, it wasn’t as easy to “wing mathematics” anymore and when it came to method of understanding such as inquiry and discovery I could only think that if my teachers would have utilized these strategies more, I would still be an exceptional math student…maybe:)

Screen Shot 2017-01-11 at 11.17.22 AM.png

Photo Credit: via Google; Ted

Growing up anytime I talked about mathematics, I was constantly compared to my Dad, who strives in mental math, versus my mom who didn’t. This is the attitude of many household, of being “I wasn’t good at math, so it’s okay that you aren’t either” and this mentality would be carried into the classroom. In high school I tutored a student with this mentality, they were the hardest on themselves, constantly saying “I’m not smart enough” or “there’s no point in me doing this, everybody knows I not graduating” and finally one day I told them to stop saying that, that they were smart enough and that if nobody else believes in you, then you have to believe in yourself. After that it was weird because I saw the switch go off, they stopped saying that they weren’t good enough and the work they put in allowed them to graduate. All that student needed was someone to believe in them and all of a sudden they gain confidence in their abilities, in order for the negative math mentality to diminish.

Treaty Education

It is sad to see that this is a reality for most teachers when discussing Treaty Education. Whether this be because of the lack of understanding and “old perspectives” it is something that many teachers and students face. The person in the email has a tough road ahead because they don’t have much support within the school to bring attention to the need of Treaty Education but this should in no way stop them from continuing these lessons. The only thing this intern can do is provide opportunities for students to learn about the perspectives of First Nations  people of Canada. These opportunities may result in failure or success but either way students and teachers will learn from these opportunities.

What is the purpose of teaching Treaty Education content? Where do I begin. Understanding where Treaty Education began is key to understand where we are today. As Canadians, we need to acknowledge and respect the First Nations, Metis and Inuit perspectives that have shaped our country. Also, because of the lack of Treaty Education in previous years, people have developed a negative or wrong perspectives of First Nation people. By representing First Nation perspectives in a positive light students can begin to understand the effect on their personal lives and allow them to exploring their understanding of Treaty Education.

This week, a few other educators and myself were discussing Treaty Education in the mathematical curriculum and that how there isn’t any presented in the curriculum. Well with curiosity I went to look at the curriculum myself and found that there are indicators that validate the importance of Treaty Education, for instance SS6.1 states “Explore and present how First Nations and Métis peoples, past and present, measure, represent, and use angles in their lifestyles and worldviews.” (Saskatchewan Ministry of Education, 2009, p.37). Now many people may think that this is an indicator that shouldn’t be reached and don’t realize the full potential it has. This indicator alone can set up an open task that will cover various outcomes throughout the grade six math curriculum. Treaty Education is important within the curriculum because it has shaped not only the curriculum we have today but our lives as well. The curriculum provides countless opportunities for Treaty Education to not only be recognized within a classroom but executed as well.  Also, as educators we acknowledge that we have diverse learners, whether that be in the way they learn or the time it takes them to learn but often culture is left out when looking at diversity. Students culture plays a huge role in the classroom and acknowledging the need for Treaty Education in schools is a step in the right direction.

 

 

 

References:

Saskatchewan Ministry of Education, Mathematics 6, 2009, Retrieved from [data file] https://www.edonline.sk.ca/bbcswebdav/library/curricula/English/Mathematics/Mathematics_6_2009.pdf

 

Week 8: Curriculum as Place

  1. List some of the ways that you see reinhabitation and decolonization happening throughout the narrative.

Decolonization and reinhabitation  is continuous throughout the narrative because of the importance of these words in the culture of Aboriginal peoples. Reinhabitation is acknowledge immediately with the featured 10 day river trip. Learning from Place: A Return to Traditional Mushkegowuk Ways of Knowing suggests “…this connection to nature and land was all the more significant for its contributions to an additional dimension of development: the cultural identity of the people.”  (pg. 70). The experience of the river trip had both youth and elders function in their environment and make connections with the nature and land. This connection and experience allows youth and elders to learn from each other and deepen their understanding of relationships with the land and their traditions. Decolonization also happens throughout the narrative as the entire experience is developed to enhance the knowledge and relationship between the youth and their elders.

” Elders would share knowledge with youth about ways to live off the river and lands and note key sites along the way. As part of the project, youth and Elders travelled together on the traditional waters and lands, exploring history, language, issues of governance, and land management.” (Jean-Paul Restoule, Sheila Gruner, Edmund Metatawabin, pg. 75)

  1. How might you adapt these ideas to considering place in your own subject areas and teaching?

Inquiry learning is a huge part of physical education and mathematics which allows the involvement of reinhabitation and decolonization to occur. Place is often more used in physical education because of the emphasize on creating and developing oneself through the environment. This also contributes the board areas of learning that are building lifelong learners, building engaged citizens and building a sense of self and community. These three areas can be developed with the students relationship with place. Also, recently we were in a classroom where the teacher brings in students parents if they work in the area that she is teaching in order for the students to be engaged with the concepts. Therefore, by reaching out to people that are more experienced in the field of study allows for a deeper knowledge to be taught. For example, in mathematics an accountant could come in to relate to statistics and finances.

Jean-Paul Restoule, Sheila Gruner, Edmund Metatawabin, Learning from Place: A Return to Traditional Mushkegowuk Ways of Knowing, 2013)