Week #12 Reflection

To begin  I must say I cannot believe that this marks the end of our mathematics course. Over the duration of these past twelve weeks I feel that I have made tremendous growth in my level, attitude and mind set towards mathematics. Prior to the commencement of the course I was anxious and unsure if I would be a suitable mathematics instructor for I felt my confidence and skills greatly lacked. One of the more valuables lessons I have learned is that ALL individuals, no matter age, gender or abilities has the power to learn, love and understand math. Our classroom lessons focused heavily on the deconstruction of the once “accepted” method of teaching math and encouraged a new wave of instruction. As a future mathematics instructor it is my responsibility to work together with my students to develop their skills level in order to demolish the negative connotation surrounding mathematics.

In my final week of my observational placement I had been given the opportunity to conduct my first mathematics lesson, and let me tell you it was not as scary as I imagined it would be. My associate teacher and I co created a data management lesson which focused on enhancing students understanding of terminology so that their ability to develop effective graphs would increase. To begin we introduced students to the "Frayer Model", an organizational tool used to categorize knowledge regarding various concepts. To introduce this model we played a game where I concealed the middle word and filled out each category to provide a description of what the word was.  Once this was complete I showed another slide and explained each category focusing on the differences between each category and why information is inputted into each section. Finally we collaborated as a class to sort out and categorize information regarding the word “Rocks” -a concept they had been studying in science. Once I felt that students had a thorough understanding of how to use the model I explained to them what they would be doing during the lesson. My associate teacher and I extracted six key terms (Axis, Table, Talley, Scale, Graph, Bar Graph) which we felt were necessary to build students understanding around data management.  

Students were split into six groups of four and were responsible for building a Frayer model based on their assigned word. To begin, I had students work independently to gain a sense of their knowledge on their term. After about ten minutes students gathered in their groups to produce their Frayer model on a graph piece of paper. It was amazing to see the different interpretations and understandings brought forward by each student, as well it was astonishing to watch students learn off of one another. The collaboration of ideas allowed the more timid, quite pupils to work together with the more knowledgeable students to heighten their understanding.  

The exchange of conversations were fascinating as each student appeared to have a multitude of ideas and opinions in regards to their concept. When this was complete the students then displayed their final product and participated in a "gallery walk" where they had the opportunity to look over at each others work, record what they had observed and provide constructive feedback for their fellow peers. I felt that this activity was an amazing success as the students truly gained a great sense of knowledge in regards to data management terminology. 

Math does not have to be scary, instead it can be something which kids can look forward to and be excited to learn if structured well. Never would I have thought that the activity I created would be suited for a mathematics lesson however it was incredible to watch the progression of knowledge.This course has truly opened my eyes to the wonder which can come from a mathematics classroom and know that I will continue to work on my skills so I can continue to build my knowledge.

Week #11 Reflection

This week in out mathematics class we discussed data distribution focusing particularly on probability. We began with the implementation of our own experimentation questioning and testing the likelihood of an individual collecting six different prizes distributed amongst several cereal boxes.  To carry out the experiment we were given a dice and recorded the rolls which were produced. The goal of this activity was to roll each number once to gain a better understanding of the likelihood of collecting s ix separate prizes.  It took our table group a total of twelve rolls to produce each number once however there were multiple times were a number appeared more than once. This experiment increased my overall understanding of how data management and probability intertwine as well exemplified the utilization of mathematics in our everyday lives.

To continue our discussion we furthered our investigation of the data base “Tinkerplots” focusing on how educators can utilize the resource in the classroom to graph gathered data. The video we examined investigated the probability of the numbers two and three appearing when two dice are rolled over a consecutive amount of trials.  The database displayed the continuous data generated and inputted it into a graph to allow users to observe the amount of times each number was produced. After numerous demonstrations our class collaborated to discuss the results and consider the academic benefits which may follow from incorporating the resource into classroom study.  Through our ongoing investigation of the resource “Tinkerplots” I have come to the conclusion that the resource acts as a valuable outlet which can significantly increase users overall understanding of data management skills through the multitude of visual representations provided.

To conclude our lesson we discussed the importance of developing and implementing effective ongoing assessment of student learning. Assessment for, as and of knowledge is a continuous practised process which signifies to educators a student’s academic progressions and/or failures in different subject areas. In addition, the implementation of ongoing observations indicates to educator’s necessary modifications and/or accommodations of activities to heighten a student’s ability to succeed. In addition we discussed the importance of classroom educators providing a multitude of skill developing activities so that students have numerous opportunities to demonstrate knowledge and understanding. As a future educator I recognize that assessment of learning cannot only be based solely off of testing of skill instead it is important that we provide students with multiple opportunities to demonstrate learning progression. To further my understanding I viewed a TedTalk which spoke about assessment within the classroom and the responsibility that we as educators take on.

 Assessment of student thinking, knowledge and understanding becomes a critical token for their ability to succeed in all realms of study. When educators become equipped with effective assessment tools they are better able to identify their student’s areas of strengthens and/or weakness allowing them offer better educational support.. As a future educator it is my responsibility to inform myself on the expectations of diagnostic, formative and summative assessment so that I am able to provide learners with a successful learning environment. For many students mathematics becomes one of the more difficult areas of study to develop therefore educators must provide ongoing support to promote and nurture academic growth. Through our collaborative class discussion and study of numerous evaluation examples I feel this lesson significantly contributed to my understanding of providing continuous effective evaluations of student learning. 

Website for Images:
http://images.clipartpanda.com/dice-clip-art-LcKeAjBca.jpeg
https://www.google.ca/search/data+management&biw=1366&bih=667&source=lnms&tbm=isch&sa=X&ved=0ahUKEwjni5SvxrjJAhXMHh4KHd5TB40Q_AUIBigB#tbm=isch&q=bar+graph+clipart&imgrc=LQgNPttllbxv7M%3A

Week #10 Reflection

This week in our mathematics course we discussed mean, median , mode and range,   integral concepts which become infused in the everyday lives of an individual. We began by looking at the development and organization of a stem and leaf plot through an estimation activity which involved a jar full of Oreos! I generated my guess by imagining about how many Oeros came in a standard package (48) then visualized the amount of boxes required to fill the jar. I hypothesized about one and a half boxes which would calculate to 72, once the class formulated their estimations we organized the data on a stem and leaf plot. When we input the data onto the graph we were able to calculate the mean, median, mode and range which produced numbers quite similar to the actual amount (106).  This activity was a fun, informative demonstration of how information can be gathered and organized to produce a set of data.

Figure 1
Found under the Statistics tab for students.
 These are more activity based games
 as they work to challenged student thinking
in a fun way.

For this week I thoroughly enjoyed being introduced to and having the opportunity to explore the website “Johnnie's Math Page" as it had an abundant amount of activities available for both students and teachers. This website was unlike any other we have explored so far as it focused less on games but more on activities which can be used to enhance user’s comprehension of different mathematical concepts. I began by investigating an activity which explored inputting collected data presented on a tally chart onto a bar graph. Through the games simplistic nature, in-depth instructions and explanation of different mathematical terminology this resource is one which I would suggest colleges and students. To continue my examination I looked at the resources available for educators and developed my own pie graph where I inputted data which demonstrates the makeup of activities I do in one day (Figure 3).  This resource was a fabulous outlet to investigate as it was not complicated to create a graph. As a future educator I foresee myself utilizing this resource in the classroom for I predict it provide a multitude of assistance for students.

                                                                         

             

The classroom activities presented this week were quite interesting as they were done online through the resource “Gizmos”. This resource allows users access to a multitude of different activities created by a classroom instructor. Students are able to join a classroom and participate in the different resources made available. Over the years the advancement of technology has significantly shifted the face of the traditional classroom. Numerous programs such as “Bring Your Own Device” have been implemented to encourage the exploration of different digital outlets within the classroom in order to promote individuality, creativity and success. The rapid influx of technology has altered the pace and method in which individuals learn, process and retain information and as a result educators must be willing to shift traditional practices and ways of thinking in order to offer the most for their students. The classroom activities provided allowed for a greater exploration of different digital outlets available which becomes essential in our understanding of our role as a twenty first century educator. We must incorporate activities offered online for it will provide students with the greatest opportunity to grow and succeed.

Week #9 Reflection

This week in our mathematics course we carried on our conversation in regards to different shapes however we focused more on the concept of discovering the area, perimeter and volume of an object. Measurement in particular, area and perimeter are concepts which I hypothesize students would gain the most adoration and appreciation for as these units can be applied to multiple strands in their everyday lives.  As I have discussed in previous blog posts one of the more important things an educator can do for their students is make math relatable. We must demonstrate to students that what we are teaching them will largely impact their overall development in society and academically.

To continue our lesson we were introduced to the concept of the guided inquiry process and provided with an example of such activity. The guided inquiry process emphasizes student learning through investigation and exploration of activities which aim to challenge individuals understanding and promote a higher level of thinking. The guided inquiry process challenges a student’s level of evaluation and allows for a more analytical thought process. When educators introduce the inquiry process into their classroom they promote learning through investigation and questioning which works to expand knowledge. I thoroughly enjoyed participating in this inquiry based activity as I felt it expanded my understanding of the utilization of measurement within contemporary society. As a future educator I foresee myself incorporating different inquiry based activities, such as the one provided, in my classroom for I feel students will benefit significantly. For a student to thrive educators must undergo constant assessment of their skills by providing a multitude of skill based activities such as the inquiry based ones.

For this week I enjoyed the games provided however I wanted to continue searching for different resources. While conducting my search I came across the website “Adapted Mind Math” which provides users with a multitude of activities for different units of study. To begin you select the grade level you wish to explore, I selected grade 6, then you pick the lesson you want to participate in, I choose geometry and selected the activity “area of a square.” In this activity users begin by selecting their character then are given the instructions for the game. The goal for the activity is to complete each level by answering a multitude of questions, dealing with area and perimeter. What I enjoyed most about this game is that users were not timed they had the ability to thoroughly think out what was being asked of them and the questions increased in difficulty after the completion of each level. As well, when a question was answered incorrectly users were informed were they had gone wrong. I definitely see myself introducing this resource to my students as I feel they would truly benefit from it.

 Figure 1

The selection of units and activities which individuals can select to explore.

Figure 2

When users get a question right this is the message which is shown. As questions are answered correctly users are given points which can be used within the game. 

Figure 3

When users answer a question incorrectly, the website provides an in depth explanation of where they went wrong as well thoroughly demonstrates how  to arrive to the correct answer. This is fantastic for users as they  have the ability to understand how to fix where they went wrong.

To conclude I thoroughly enjoyed this week’s mathematics lesson as it opened my eyes to the importance of incorporating inquiry based questions within the classroom. Educator must continually expand their set of knowledge and undergo constant assessment off practises and techniques.    

Link to the website "Adapted Mind Math"

http://www.adaptedmind.com/

Link to Image
www.pinterest.com/inquirybased

Week #8 Reflection

This week in our mathematics course we covered the unit regarding the classification of different shapes. During my academic career this unit had always been a favorite of mine as I found it most relevant to my everyday life. Unlike fractions, I had the motivation to strengthen my understanding and further my knowledge which made my experience as a student a lot more meaningful.  Throughout the course of our studies one of the most memorable and valuable lessons I have learned thus far is that students perform the best when they understand how math relates to their everyday life. For many students mathematics is an intimidating, difficult subject to comprehend and practise as it presents numbers in unfamiliar, complicated ways.  An educator becomes a student’s primary unit of care therefore they must take the time to work and build trusting relationships so an individual can turn to them in times of need.

When educators take the time to relate these ideas into everyday situations a student’s likelihood to remember a concept greatly increases.  This idea has been demonstrated both in my placement and in my mathematics class. Similar to our math class, last week in my placement classroom the teacher introduced the concept of the line of symmetry and began  by showing a picture of a pie then dividing it in half to show how the line of symmetry works. She continued by asking them what other objects could we cut in half to create two equal parts and numerous students volunteered different answers.  At the end of the lesson the teacher collaborated with the students and asked how the line of symmetry worked and every student had their hands raised high in the air and the one asked to speak referred to the idea of cutting a pie in half to create two equal pieces. The students appeared more interested and enthusiastic to listen and participate when they could relate the concept to their everyday life.

 During our mathematics classroom, similar to every week, we had different presentations of activities related to the unit we were learning.  We have generated a collection of numerous effective activities for individuals ranging in age and abilities.  This session a colleague introduced a fantastic activity which I foresee myself incorporating into future lesson plans. The activity featured the comical, popular animated figure Mario which immediately heightened the interest and excitement in every student. The sheet presented various characters related to the Mario game and we were instructed to illustrate the symmetrical figure of the character. This activity was very simplistic in nature which allowed for the expansion and exploration of individual creativity. I have to say, the completion of this activity was one of the first times I have ever enjoyed completing a math activity! Unlike past, traditional methods of instruction educators cannot present redundant complex questions which aim to challenge and evaluate a student’s level of knowledge.  If a student cannot develop a foundation of knowledge there is no point in aimlessly forcing information down their throats.  It is also important to remember that an activity should not be too complex in nature as it may lessen an individual’s willingness to improve.

Figure 1

As you can see I need to continue working on my drawing skill, but none the less this was a fantastic activity which individuals of all ages can enjoy. 

Math, like any subject is one which requires constant development and change. There is no one absolute way to learn or teach it therefore as educators we must be willing to work on improving our own skills and practises. Over the course of our mathematics course I have gained what I believe to be a great deal of knowledge and understanding on how to become an effective educator. When we give students the chance to think independently we fuel their ability to thrive.

Week #7 Reflection

This week in our mathematics course we focused on patterning and algebraic expressions, units which become integral towards a student’s overall success in their academic career.  Students are introduced to these concepts at a young age for they lay the foundation for problem solving and recognizing changing number values. An individual’s ability to recognize and describe patterning expressions becomes fundamental towards building their comprehension of mathematics as well strengthens their ability to solve algebraic equations. Patterns are represented in a multitude of ways and can range in rhythm, design and simplicity.  For example younger grades begin their studies by examining patterns, such as the one demonstrated in figure one, to determine the rhyming scheme. As the student progresses into a higher grade level they move onto more thought provoking expressions, such as the one presented in figure two, where they are expected to recognize the relation between the figures and create an algebraic expression.

Figure 1

 Figure 2

Similar to fractions the largest struggle a student may face when dealing with patterning and algebraic expressions is that an equation is represented in an unfamiliar way. Letters are used to represent a value of a certain expression which may be confusing for some who are unable to gain a concrete understanding of the concept. Our classroom discussion focused on the importance of providing different manipulates and visual aids for students in order to strengthen their comprehension. When educators provide students with the tools to develop they encourage and support their ability to succeed academically. Algebra is not an easy concept to grasp for students therefore as an educator I realize the importance of working from the bottom up to develop and strengthen an individual’s skill level.

While searching online for different resources and games I came across one which stood out to me. The game was taken from the website MathFox which provides a variety of interactive online games for students varying in age, grade and skill level. The one which I selected dealt with algebraic expressions however presented very basic questions at the beginning. Each time a question was rewarded correctly students gained one hundred points and had the opportunity to “attack” the fellow pirate ship. This game would be ideal for students in the grade 4/5 level or those who struggle to grasp the fundamental elements of what algebra entails. I really enjoyed this game as I did not feel rushed nor pressed to finish a question within a certain time frame, I had a chance to think about what was being asked of me and to confirm my answer.  Games become an integral component to ensuring academic success and growth within students as they strengthen their skills by demonstrating problems in a “fun” way.

As a student my greatest struggle with mathematics was creating and solving algebraic expressions. It was something I was not familiar with, and often found it difficult to find the relationship between two dissimilar numbers. Through my own personal experiences, the readings provided as well our classroom discussion I have learned and better understood the importance of teaching students the “basic” skills of patterning in order to improve their understanding of algebra. If students do not have ab understanding of the preliminary skills it is illogical to expect them to understand the more complex, complicated units. 

Week #6 Reflection

This week in our mathematics class we furthered our investigation on the topic of ratios, rates and proportions. To begin we were given different questions which we worked on independently and then reconvened as a group to discuss different ideas produced and thoughts generated. This is a great technique for instructing as it gives enough room for both independent work and group discussion. We continued our lesson by looking at the how rational proportions are similar to fractions in that they are used to compare or relate numerical values that are equal to one another. Similar to fractions this unit presents numbers in an unfamiliar for many individuals therefore it is important that educators take the time to provide students with a variety of methods to compute and understand what is being taught. To benefit the greatest amount from a lesson an educator must make a lesson practical and relatable for their students. When a student feels that what they are learning is beneficial towards their everyday life they are more likely to succeed and be inspired to learn.

This idea was demonstrated in our lesson when we were introduced to “Joels Kitten Problem”. This activity required individuals to work together in groups of two to four and come up with our own method to solve the problem. As a group we were responsible to solve the question and write out our steps with clear details on a piece of chart paper. When this was complete we joined up with a new group were we were responsible to instruct others on what we had done and communicate our way of interpretation and thinking. The benefit of this question was that it was open ended, it allowed for a variety of unique solutions and thinking techniques, as there was not a definite way to produce an answer. This method of teaching was informative as it was fascinating to observe the variety of thinking techniques. For example my group solved the problem through trial and error whereas the group we partnered up used fractions (Figure 1). Although our techniques were completely different, we both came up with the same conclusive answer. I thoroughly enjoyed participating in this exercise as listening, explaining and communicating with fellow peers not only strengthened my knowledge but expanded my overall understanding of the lesson.  As a future educator I anticipate including this technique in my classroom as I feel that students learn best from one another and benefit when they are put in an instructional position.

In my prior blog post I discussed the importance of including interactive, educational games into a lesson in order to satisfy the twenty first century practice of learning.  This week I explored the resources provided by our professor however continued to explore the outlet as I wanted to see what else the website offered for users. One game which I found particularly interesting was “Ratio Blaster” (Figure 2) an interactive game which worked to enhance students understanding of rational equations. Users are given one minute to complete as many equations as possible in order to proceed to the next level.  When a question is answered correctly the ships you are shooting at remain still however answered incorrectly the spaceships move closer to your shooter. The equations were not complex and when answered incorrectly, the correct answer was demonstrated. Unlike the resource “Orbit Integers” I explored last week this game was not a race, which may be beneficial for students who cannot handle a more fast paced game as well when a question was answered incorrectly a new solution was not produced instead the same question was asked which allowed individuals to fix their wrongdoings. As twenty first century educators it is our responsibly to introduce students to the abundant amount of resources available to them. We must take the time to discover different resources as they will have numerous benefits within a classroom.  

Figure 1

A screenshot of my group and a peers group solution to the question presented in class. Both solutions demonstrate a wide range of thinking however the final answers produced are similar.

Figure 2

A screen shot of "Ratio Blasters" users aim to "shoot" the correct answer for the question provided. The space ships lower when a question is answered incorrectly until they reach the users blaster.

Link to "Ratio Blasters"
http://www.mathplayground.com/ASB_RatioBlaster.html