Reflecting on What I Have Learned- Final Math Blog

     As I finish attending my final mathematics education class for the year I end an enriching learning experience and begin to create new ones as I continue to develop in my growth as a teacher. However, when I finished the last class I got the opportunity to reflect on what I have learning and how I have grown as a mathematics education teacher. The concepts and strategies that I learned about are too numerous to write in one blog post, so I would like to focus on the big ideas that I learned and how I can use this in my own instruction.

     The first big idea that I learned about that drastically altered my approach to teaching math was having a growth mindset which believes that anyone can be successful at math. I remember how many of my teachers when I was in school telling students that some people are naturally good at math and some are not. While there may be students who excel at math with little effort, there is no research to show that some students do not have the possibility at doing well in math. As a teacher I know it is important to instill this into my students and help them believe that with hard work any student can be great at math. This also meant that I needed to change my mindset from thinking that I would never be good at math to believing that if I work at it then I can be successful.

     Before this class I believed that math was about using specific formulas and algorithms to get to a solution. I was always taught that there was only one way to arrive at an answer and the formulas will help you get there. I have come to learn that this is horrendously false. Often in many problems there are various ways to get to a solution with a variety of algorithms to get there. As teachers I have learned that we not only need to recognize this idea, but also have the ability to anticipate how students can arrive at a solution. Teachers need to do this in order to know if this process makes sense and if it can be applied to all similar problems. To do this, teachers need to be thorough in their preparation by creating multiple ways to arrive at an answer to a problem. All in all, I have learned about how I should encouraging students to be able to get the same answer in different ways and not confining them to one particular algorithm.

     Perhaps the most important role of a math teacher is developing effective questions and creating open problems to develop the math knowledge of each student. One thing that I learned about open problems is that they should have a wide base and a narrow ceiling. This means that problems must be simple enough so that every student can begin to work on it, but hard enough so that every student is challenged. As the classes went on we got numerous examples of what this looks like by performing questions that every student would be able to answer, but can be difficult enough for those who want to challenge themselves. By doing this, no student feels like they are not able to participate and every student can be engaged with the lesson.

     On top of creating open questions, teachers must also ensure that these questions get students to go deeper in their thinking and challenge their knowledge on the concept. One interesting way to do this that we learned about in our classes is creating open questions with little information to get the students to ask for the information they need in order to complete the task. For example, if a question asks how much can fit inside a square then a student should ask for the dimensions of the square to calculate the area. Instead of students always being handed the information and asked to solve, teachers should get students to develop their ability to question problems in order to find a solution. Questioning is also a way to lead students who are struggling to figuring out math concepts on their own. One piece of pedagogical knowledge that I have learned to apply in my teaching is guiding students to a self-revelation or self-discovery rather than simply giving the answer and showing the process to get there. Questions are a great way to accomplish this goal because the right questions can direct students to think about different aspects in order to get to the right path. I remember too many times in my own education that my teachers often taught me by showing the answers and teaching how they got there. I have realized how ineffective this method and that teachers need to educate students by leading them to learn on their own rather than just being the only source of information.

     Finally, the final big idea I want to discuss is that learning in mathematics should be interesting and interactive. This means that problems given to students should be relevant to real life, but also should include something that students can relate to in their lives. For instance, during this time teachers could ask questions that are connected with the holiday season. I also learned that math should be taught in a way where students can interact with what they are learning. This can be done by using physical manipulatives that students can use to explore. For example, in class we got a chance to use various manipulatives that can be used to teach fractions including cut up plates, clocks or shapes. This can help the students visualize what they are learning and use it to apply to problems while making the learning much more interesting than traditional drill and practice methods. It is well known, that students retain much more when they are interested in what they are learning.

     Although this short blog post only begins to explain my development as a mathematics teacher it does present my reflections on the big ideas that I have learned. I have learned that teachers need to be the guides directing students to their learning rather than just telling them how to solve problems. I believe that everything I have learned in this class will help me be a better teacher which directs students to be as successful as they can be. 

Data Management and Probability

     Data management and probability are perhaps two of the most practical yet sometimes forgotten topics in math, but this became the focus of my mathematics education this week. We learned about how to teach students to understand the probability of situations and how to take this information then plot it on a graph. In order to understand these two topics we performed an activity which combines the two. We first estimated the number of Oreo cookies in a jar, wrote down our estimate, then placed our estimate onto a stem and leaf plot. With all the estimates laid out onto the plot we could determine the mean and mode of this data set. This interested me because I did not really understand the purpose of a stem and leaf plot, but this activity demonstrated its practical uses. I believe that when teachers do this it grabs the attention of the student and helps them remember what they learned because they can trace the example back in their memory in order to remember this topic. I know that when I was student I learned at my best when teachers provided me with practical examples of how what we were learning being applied to real world scenarios.

     We also began to perform some activities to exercise our knowledge of probability. For example, we rolled dice until we got to every number on the dice in one set. This demonstrates to students how many variations can come in this particular situation as one group only needed 12 tries while another needed 36. Games are an excellent way to get students’ attention and can be an excellent starting point for an educational conversation. For instance, if I was doing this activity with my students then I would discuss with them the odds of receiving a certain number. The textbook reading also provided a number of interesting ways to teach this topic using manipulatives. One was a spinning wheel labelled with various colours and the students would have to predict the probability of landing on a particular colour. Cards are also another fun way to teach this task, as the textbooks shows us, because it allows for discussion on different scenarios and the probability for each. I think that this would really grab the attention of the student because it is an object that they have seen frequently, one that is familiar to them.

     One deep idea that truly resonated with me this week is that we need to teach our students skills that will help them in everyday life. One of these skills is estimation, a skill that many teachers tend to neglect. I remember how so many of my teachers taught me about formulas and how important they were to memorize, but let’s face it, this is not what we are doing in our everyday lives. Students need to learn how to estimate and predict certain scenarios in order to make educated decisions. As teachers, we need to show students how to perform this process and how to analyze a scenario to make the best decision. 

Independent Lesson Plan

NAME: Zachary Gill
Grade:  7	Subject: Language Arts	Strand(s): Writing, Reading
Overall Expectation(s): Writing: 1. Generate, gather, and organize ideas and information to write for an intended purpose and audience. Reading: 2. Recognize a variety of text forms, text features, and stylistic elements and demonstrate understanding of how they help communicate meaning.	Specific Expectation(s): Reading: 2.2 Analyze increasingly complex texts to identify organizational patterns used in them and explain how the patterns help communicate meaning. 2.4 Identify various elements of style – including foreshadowing, metaphor, and symbolism – and explain how they help communicate meaning and enhance the effectiveness of texts. Writing: 1.1 Identify the topic, purpose, and audience for a variety of writing forms. 2.3 Use some vivid and/or figurative language and innovative expressions to enhance interest.	Achievement Chart Categories:         Knowledge & Understanding         Thinking         Communication         Application
LEARNING SKILLS AND WORK HABITS: Which LSWH(s) will be addressed?   Responsibility       Independent Work         Collaboration         Organization        Initiative        Self-Regulation Responsibility: Students use their class work time responsibly to read the assigned writing pieces and complete their own poem. Independent Work: Students are able to work and complete the assigned tasks with limited supervision and without the assistant of the teacher to get started. Initiative: Student is willing to take risks and begin the task by developing their own ideas and creating a poem to express them.
LEARNING GOAL(S) Describe the curriculum expectations & LSWH  in student friendly language We are learning to identify the organizational structure of a haiku poem. We are learning about how we can organize and express our ideas through poetry. We are learning to create poetry that uses various elements to make it interesting.	ASSESSMENT TASK /STRATEGY Describe what students will be doing to address the learning goal(s) and identify:         Assessment of learning: After reading poems written by various authors students will create a basic haiku poem with the appropriate structure.              It will be a summative assessment to wrap up the lesson.	SUCCESS CRITERIA Describe what successful attainment of the learning goal(s) looks like for your assessment task I can create a haiku poem with the proper organization. I can recognize the structure in a haiku poem written by other authors. I can write a haiku poems with various writing elements to help create meaning.
ASSESSMENT TOOL    Anecdotal Record, Rating Scale, Checklist, Rubric, Other         A checklist will be created based on the success criteria to see if students can meet the criteria.

Assessment Tool

Criteria	Standards Met	Standards Not Met
Haiku poem follows basic structure of 5 syllables, 7 syllables, 5 syllables.
Haiku poem uses writing elements to make it interesting (example imagery, similies, etc)
I can read haiku poems by other authors and understand what elements they used to create meaning.

Learning and Assessing

     One of the most discussed topics in education because of its great importance on student learning is assessment. This topic was the focus of my mathematics education class this week. Using the clapping activity as a demonstration, all the students in my class got an opportunity to understand the importance of establishing learning goals and success criteria for students. It was an example of how students can improve if they are given descriptive feedback which outlines some areas for improvement. After this we began to discuss the importance of setting learning goals and what these goals need to look like.

     I learned that learning goals are important because it gives students a target for them to strive towards. I remember many times when I was a student being frustrated when I received a grade that I was not content with because it did not know what I had to do to get a good mark. I believe that it is critical for teachers to outline clear goals for their students so that they know exactly what they have to do to be successful.

     We also learned that learning goals must have certain characteristics. They must not only by specific to curriculum expectations, but must also be accessible to students using language that they understand. In addition, they must be filtered through a big idea and rooted in conceptual understanding. All in all, I felt that it was most important for me to understand that learning goals must be clear and effective for students to know exactly what it is they must do in order to be successful.

Here is a link to a website with resources that we were to explore this week which helped me to understand how to create effective learning goals: http://www.edugains.ca/newsite/aer/aervideo/learninggoals.html. 

     I also want to discuss my learning activity presentation that I conducted this week. Although the presentation did not go as smoothly as I hoped, I still received an insightful learning opportunity. I learned about creating an activity which can not only get students engaged with the topic, but also teaches them about the concept (which was Pythagorean Theorem in my presentation). For my presentation in particular, I also got to see how technology can be incorporated into instruction. My application allows students to visualize how Pythagorean Theorem works by expanding and shrinking the sides of the triangles while seeing the hypotenuse change accordingly. In addition, I learned about how I can use an app like this to help students solve real-world problems. I wish that this was done during my education because I enjoy a visual of how math concepts work and how it can be applied to everyday life. Overall, I believe I can use this experience and learn from it so that I can create more effective tasks for my own students that will help them grasp the concepts I am teaching. 

AER Strategy Form

EDBE 8Y01 Digital Portfolio: AER Strategy Form                  Name: Zachary Gill
GROWING SUCCESS POLICIES	My Professional Learning Goals 1 goal for each	Strategies For Meeting My Goals 1 strategy for each	Curated Resources minimum of 2 sources for each
POLICY Fundamental Principles	My goal is to learn how to create assessment tasks which address multiple curriculum expectations, but is clear to the students about how they can succeed.	Discuss with my associate teacher and find resources to learn about how to write using student friendly language in my success criteria or learning goals.	Learning Goals and Success Criteria: Retrieved from http://www.edugains.ca/resourcesDI/ProfLearningModules2011 /DiffInst_AssessmentandEvaluation/LearningGoalsSuccessCriteria ViewingGuide2011.pdf Make it Measurable: Set Clear Goals & Success Criteria for your Projects: Retrieved from http://www.disambiguity.com/make-it-measurable/ Co-Constructing Success Criteria: Retrieved from http://www.cea-ace.ca/education-canada/article/co-constructing-success-criteria
POLICY Learning Skills & Work Habits	My goal is to learn about how to assess learning skills and work habits by learning about what these learning skills look like.	Gather resources that go into more depth about what these learning skills mean and observe the students during my teaching block to see if I can assess them.	Sample Checklist of Learning Skills and Work Habits: Retrieved from https://portal.ddsb.ca/class/l4bn1yz/Lists/HandoutsandMaterials /LearningSkillsStudentSelfAssessmentChecklist.pdf Learning Skills: https://www.pinterest.com/pin/546342998525953415/ Learning Skills and Work Habits: Retrieved from http://www.edugains.ca/newsite/aer/collaborativeinquiryproject/ cipquestions/LearningSkillsandWorkHabits_HPEDSB.html Using Assessment and Evaluation Strategies to Support Students Retrieved from: https://www.youtube.com/watch?v=-wePut0cfzA
POLICY Performance Standards: The Achievement Chart	My goal is to learn more about each achievement category and learn about how these categories can be addressed in every lesson.	Search for resources that will help to gain a deep understanding of each category and what it looks like in the classroom.	Performance Standards: The Achievement Chart: Retrieved from http://www.yrdsb.ca/AboutUs/ReportingStudentAchievement/ Documents/ParentBrochure_AchievementChart.pdf Actions Verbs: Retrieved from http://beta.edugains.ca/newsite/aer/eModules/courseEngine/ actions_verbs.html Ontario Curriculum (Section on Assessment and Evaluation of Student Achievement)
POLICY Assessment FOR Learning & AS Learning	To find out about when each type of assessment is necessary and how it can be implemented.	Find resources that will list examples of assessment tasks that address each type and discuss with my associate teacher about what she does.	Co-Constructing Success Criteria: Retrieved from http://www.cea-ace.ca/education-canada/article/co-constructing-success-criteria How Should We Measure Student Learning? 5 Keys to Comprehensive Assessment: Retrieved from https://www.edutopia.org/comprehensive-assessment-introduction. Every Teacher’s Guide to Assessment: Retrieved from http://www.edudemic.com/summative-and-formative-assessments/ Types of Classroom Assessment: Retrieved from http://www.learnalberta.ca/content/mewa/html/assessment/ types.html
POLICY Evaluation	I want to learn more about the process of collecting and assessing student work to evaluating them with an overall grade. In addition, I want to know about what to do if a student hands in little or is failing to meet curriculum expectations.	Find resources from school boards (especially the one I am a part of) and determine what their grading policies are.	Student Assessment, Evaluation and Reporting in Peel Elementary and Secondary Schools: Retrieved from http://www.peelschools.org/trustees/boardpolicies/Documents/ Policy%2014.pdf Assessment, Evaluation and Report in Elementary School: Retrieved from http://www.peelschools.org/parents/helpyourchild/reporting /elementary/Pages/default.aspx.
POLICY Reporting Student Achievement	My goal is to become more familiar with the structure of reporting and how assessment collection data is plotted onto it.	Find resources or discuss with teachers in my placement school about how to fill out report cards.	Associate teacher and other staff at practicum school. Sample report card templates: http://www.edu.gov.on.ca/eng/document/forms/report/card/reportcard.html List of resources and generators to create report card sections: http://www.ontarioreportcards.com/ontario-report-card-resources.html Progress Report Cards: Retrieved from http://www.ontarioreportcards.com/ontario-report-card-resources.html
POLICY Students With Special Education Needs	My goal is to learn about different methods of modification, alternative learning, or accommodations and how they are created to suit a students needs.	Research with the purpose of discovering various examples of accommodations and modifications to help me understand this topic.	Learning for All Textbook: Bennett, S., & Dworet, D., with Weber, K. (2013). Special education in Ontario schools. (7th ed). St. David’s, ON: Highland Press. Modifications, Accommodations, and Differentiated Instruction: Retrieved from https://www.goleaps.com/articles/differentiatedinstruction Accommodations and Modifications: Retrieved from https://specialeducationontario.wikispaces.com/file/view/Modifications+and+Accommodations+by+Jacki+Oxley.pdf
POLICY English Language Learners	My goal is to find out what strategies are used to teach students who know little English.	Since my school board is so diverse (Peel Board), I want to look up the policy for ELL students.	http://www.peelschools.org/parents/programs/esl/pages/default.aspx Student Assessment, Evaluation and Reporting in Peel Elementary and Secondary Schools: Retrieved from http://www.peelschools.org/trustees/boardpolicies/Documents/ Policy%2014.pdf Steps to English Proficiency: Retrieved from http://www.edugains.ca/resourcesELL/Assessment/STEP/STEPUserGuide_January2012.pdf
POLICY The Kindergarten Program	Discover the major differences between assessing Kindergarten students and other students.	Study both Growing Success documents and list the differences.	Growing Success Growing Success: The Kindergarten Addendum (A detailed reading of both to discover the differences)

Oral Communication Blog Post

Creating Great Discussion

Hello to my readers! This blog post will discuss a part of language arts that is often neglected, but is an integral part of the program. Students must be able to present orally and listen to the ideas of others in order to be successful. I believe that the best way to foster these skills is through student led discussion in the classroom, and this post will expand on how this can be done.

Resource Critique

One resource that I discovered to help me understand how to teach oral communication skills is one found in the capacity building series entitled Grand Conversations in the Junior Classroom. It is a document which not only outlines the importance of fostering educational discussions in the classroom, but also explains how it can be implemented. It argues that these conversations can create a much deeper understanding of the text being studied as the students discuss the key topics. On top of this, students develop their presentation skills by talking about their ideas in an articulate manner while also progressing in their listening abilities as they respond to the ideas of their classmates. It lists strategies like literature circles or congresses as platforms that teachers can use to organize the students so that they can begin their conversations. It says that it can be introduced to the students by modelling what these conversations would look like, then gradually release responsibility to the students. Finally, perhaps the most important piece of advice it gives to teachers is to not dominate the conversation, but to provide prompts which moves students toward a path of deeper understanding.

Other Helpful Resources

In order to further help me understand how I can teach effective oral communication skills I began to search for resources that could assist me.  One resource that gave me a wealth of information is an article called Oracy in the Classroom: Strategies for Effective Talk (found here: https://www.edutopia.org/practice/oracy-classroom-strategies-effective-talk). This article lists a variety of ways that teachers can create effective discussion like creating guidelines so all students are respected, differentiate in the way students are grouped from pairs to congresses, and providing students with points to talk about or tasks they must complete. One particular strategy that I found most interesting was giving roles to each student, below you will find a picture listing each of these roles and what they are responsible for.

Edutopia, September 12, 2016, "Types of Talk", (online image). Retrieved from: https://www.edutopia.org/practice/oracy-classroom-strategies-effective-talk.

However, these strategies cannot be introduced until the right culture is introduced in the classroom. This is what Socratic Seminars: Building a Culture of Student-Led Discussion (found here: https://www.edutopia.org/blog/socratic-seminars-culture-student-led-discussion-mary-davenport) as it talks about creating a classroom with discussion like they had in ancient Greece. It talks about how you can your students comfortable, how to introduce it to your students using anchor charts, and how discussion can be assessed and reflected upon in order to improve the students’ abilities.

Finally, below you will find a video developed by a teacher which lists a plethora of discussion techniques and prompts that teachers can use in order to get their students to go deeper in their discussion. It is important that student discussion does not simply provide them with a shallow understanding of the topic, but that they are prompted to get a deep understanding of what they learning.

Applying it to the Classroom

These resources are so helpful in my education on this topic because it provides me with simple ways I can introduce education discussion in my classroom. For example, I could organize my students into literature circles in order to foster discussion on a story being studied. If there are students who are not participating I could assign roles to them so that each student has a job they must complete. If the idea of educational discussion is new to a classroom that I am entering into then I could use the socratic discussion article to provide me with techniques that I can use to begin to teach educational discussion to my students. Overall, all of these resources gave me a variety of ways that I can use to create educational discussion so that students truly understand what they are learning and give every student a chance to get involved in their education.

Curriculum Expectations

Although teaching oral communication skills can be applied to any grade, I believe that the kind of discussion I have discussed in this blog post would be best suited for grade 6. I believe that the overall expectation that these resources meet is: “Use speaking skills and strategies appropriately to communicate with different audiences for a variety of purposes.” Discussion also touches on specific expectations such as: “Demonstrate an increasingly sophisticated understanding of appropriate speaking behaviour in a variety of situations, including paired sharing, dialogue, and small- and large-group discussions.” In addition, students must also be prepared to participate in discussion so it touches on expectations like: “Analyse oral texts in order to evaluate how well they communicate ideas, opinions, themes, and information.”

Blog Post #2- Growing to be Successful in Assessment

           As an educator, assessment is one of the most important aspects of your job and one of the most helpful things you can do for your students. This is because assessment is much more than a letter grade or percentage on a piece of paper, but is a representation of a student’s development in their learning and an indication of how that learning compares to curriculum expectations. Without a doubt, the most important resource that a teacher can use in order to gain valuable information regarding the topic of assessment is the ministry of education document called Growing Success. Here you will see the policies and procedures that teachers in Ontario must follow when they are assessing their students, but it has also had a tremendous impact on my beliefs about assessment.

            For the most past, Growing Success did not radically alter my views on my assessment, but affirmed many of my beliefs by explaining why those beliefs were important. For example, I strongly believe in equitable practices when it comes to assessment in that I think that students should receive assessment that is appropriate to them, not what is necessarily equal to their classmates. Growing Success how this can be done through modifications, alternative learning or accommodations. Through these principles students can attain the type of learning that suits their needs. For example, if a student has a difficulty in hearing because of an impairment than a teacher might accommodate that student’s needs by providing more visuals in their instruction rather than oral teaching.

            Another way to demonstrate how Growing Success has altered my beliefs in assessment is that I always believed that assessment was done by giving an overall grade in each subject based on the material submitted. However, Growing Success showed the importance of categorizing the material and assessing various skills as each student works through their courses. For example, Growing Success explains each category of knowledge and skills as being: knowledge and understanding, thinking, communication, and application indicated on the Achievement Chart. I remember always seeing these words in secondary school, but never really understanding why. It stresses the importance of constructing units where all over these categories are assessed in a balanced manner so that the students receive a well-rounded instruction on that unit. To continue onto this, the document lists how indicators can be used in assessment tools in order to demonstrate what it means to reach each level. These indicators helped me think about how I would describe each level to my own students.

            Finally, my most common misconception about assessment before being introduced to Growing Success was assuming that assessment was simply for evaluating a student’s learning. While that is true, Growing Success’s breakdown of assessment for, as, and of learning taught me about demonstrated that assessment is much more. For instance, it describes assessment for learning as the process of gathering evidence about the students in order to know where to begin. This would include diagnostic testing and or just simply asking students what they know about a topic before the teacher begins to teach it. However, it was learning about assessment as learning that really changed my belief about assessment being conducted solely by the teacher. Growing Success describes assessment as learning as assessment which is done by the students after it being modeled by the teacher. It also talks about how this is important because it gets students to monitor their own learning and be able to formulate what they can do in order to be successful. I now realize the importance of allowing this type of assessment because students can understand how to self-regulate their own progress and determine the steps they can take in order to be successful. I now believe that the best way for students to become successful in learning and anything that they do, is to know what success looks like. Once they do, they can begin to emulate what is required of them to attain success.

            The Growing Success document has been a wealth of knowledge about assessment for me not because it explains what assessment, but why it is important and how it can be conducted. In the end, this document has confirmed my belief on why assessment is so important in education, it is not just a method of evaluating, but it has the sole purpose of improving student learning. The ultimate goal for an effective teacher. 

Creating Effective Lessons and Tasks

     In my mathematics education class I was once again enriched with knowledge about how to develop my abilities in teaching mathematics to students. Although the topic for this week was about measurement, particularly determining the area and perimeter of various shapes, the main topic I grabbed from this lesson was how to conduct an effective lesson.

     We began the class by performing a minds on activity in the form of a game called I Have, Who Has? This activity showed me the importance of beginning a lesson with a minds on activity because it helps students get focused on learning while stimulating their thinking on topics that have already been covered. In my experience as a student I felt that too many of my teachers rushed into the lesson without giving some time to get students to dial into the subject before the lesson began. We then moved into the main activity where we completed a worksheet that gets you to answer questions about how to determine the area of a circle, rectangle, and cylinder. I found this helpful because the worksheet had clear learning goals for the lesson with the expectations that need to be met. This is important for teachers to do when planning a lesson because it gets you to think about what you want your students to learn and achieve by the end of the lesson. Finally, we then began to take up some of the questions as a class and discussed what we learned as a method of consolidation. Consolidation is important because it makes sure that every student has arrived at the same conclusion. Without it, I think that students will be confused because the lesson was not wrapped up.

     After this we participated in the learning activity presentations which involved activities which could help teach students about measurement. The activities were not only fun for students, but also displayed how the knowledge of measurement can apply in real life situations. I believe this is important because I think that students become more interested in math when they know how they can apply what they are learning to situations outside the classroom.

     As I completed the readings for the week and attended class I began to reflect on what I had learned, but also began to think about how I can create lessons for a class of unique students. This I believe is one of the most difficult parts of teaching because it is hard to create lessons to suit each student. In the article Differentiating Mathematics Instruction I found a number of interesting ideas to create lessons to suit each student. For example, it is important that I understand and welcome different ways of thinking and solving a problem. Too many times I think math teachers try to force one particular algorithm on students rather than letting them come up with one. Another strategy it mentioned that I found interesting was creating open tasks where students can decide what variables to use. With this students can make it easier for themselves if they need to so they can get started or challenge themselves if they found the work too boring. 

Here is an interesting video about how math can be differentiated to help students with different needs.

How to Build Knowledge in Geometry

     This week in my mathematics education I learned more about how to be an effective teacher of geometry to my students. For many students geometry is a difficult part of math, but is obviously essential to our everyday life. I believe that teachers can demonstrate the importance of geometry by showing them how it applies to our everyday life. This can be done by asking relatable questions for students to solve in order to see how the knowledge they have gained will benefit them later in life. However, these questions must be easy enough so every student can begin the task, but hard enough so it is challenging to all students. As the capacity building series article states, questions must be an effective means to deeper a student’s understanding, but cannot interfere with their method of learning the topic on their own.  As I attend my observation days at my placement school I realize the difficulty in this, but also the reward that comes when students get excited about completing a problem.

     This week also demonstrated to me how math can be made interesting if the right tools are used. For example, we used a Halloween theme to have a discussion on similar and congruent shapes, and the meaning of each term. This is an effective method because students will remember the lesson by the images they saw. Another example that was displayed was the reading of a children’s book on geometry called The Greedy Triangle. Here the students read about an interesting story about a triangle who continuously asked for more sides, thereby creating a new shape. The book is an effective example of how students can learn without even knowing it because they are so interested in what they are reading. Unfortunately when I was a student I do not remember my math teachers engaging my classmates and me through these sorts of fun ideas, especially as I moved up in grade levels. As a result, I became disinterested in math as it was just about boring lessons and textbook homework. I believe that teachers need to make an effort to make mathematics fun to their students. Not only will they see students who are more engaged, but also students who retain the material much better.

     The final main idea that I learned this week was that a topic like geometry needs to be taught using manipulatives. Students need to be able to physically interact with the shapes they are learning about whether it is through block tens or tangrams or whichever you choose. Here students can deepen their understanding by being able to visualize what they are learning, but are also developing other parts of their brain in the process. This is an effective way that teachers can engage students who learn in different ways and provides them the opportunity to work with the manipulatives that best suits them. This could be done through discussion or playing with the blocks or laying all the blocks and visualize in your head. Overall, it is clear that students gain a deeper learning when they are given the chance to explore. Here students can gain a relational understanding, instead of the instrumental understanding which has been emphasized far too much.