My Digital Math Portfolio Created by: Kristina Galluzzo
Table of Contents 1. Introduction................................................Page 1 2. “Math Class Needs a Makeover”................Page 2&3 3. Broken Calculator Activity.........................Page 4&5 4. Roll to Win Activity....................................Page 6&7 5. Joel’s Kitten Problem..................................Page 8&9 6. Take it to the Bank......................................Page 10&11 7. Mario’s Mirror Land...................................Page 12&13 8. 25 Best Math Apps for Kids of All Ages....Page 14&15 9. Marshmallow Madness...............................Page 16&17 10. Online Games..............................................Page 18&19 11. Number Tricks.............................................Page 20&21 12. Guided Inquiry.............................................Page 22&23 13. Frayer Model................................................Page 24&25
Introduction Mathematics is a subject of study which continues to undergo heavy criticism and disapproval from a wide audience ranging in race, gender and age. The belief that math is a subject enjoyed by few and hated by many has been ingrained into the minds of individuals and has created the idea that it is a concept which “comes easy” or “naturally” for those lucky few. This negative connotation has left many individuals, like myself, to grow anxious and nervous when having to deal with math and instead of trying to improve their knowledge they choose to ignore it all together. As a twenty first century educator it is my responsibility to demolish this negative connotation through and work to build my students understanding and appreciation of mathematics. The digital math portfolio I have created incorporates lessons and learning activities we explored during our period of study. I have gathered a multitude of diverse learning activities which I believe will allow for a multitude of academic benefits for both educators and students.
“Math Class Needs a Makeover”
https://www.youtube.com/watch?v=qocAoN4jNwc
“ Math Class Needs a Makeover” This Tedtalk features the speaker Dan Meyer who claims that “today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them”. This inspirational speaker aims to deconstruct the flawed conventions of “accepted” mathematics instruction in hopes to promote a change of values and understanding. He discusses the necessity of inspiring student thought and growth mind set by giving them the opportunity to question and test our their knowledge. He promotes the idea that mathematical equations cannot rely on universal understanding instead educators should promote students to critically and analytically think. This video is a segment towards how our mathematics class has been constructed over the course of the weeks. Our professor has inspired us to turn away from past practises and instead invite new, more thought provoking ways to enhance student learning. Over the years there appears to be a flawed conception in that individuals have been reared to believe that there is only one way to come up with a solution when dealing with mathematics. Instead of prompting individual thought and growth students are instructed to follow a specific method to find a solution so that there is a universal answer. This video is a fantastic resource for contemporary educators to study as it will heighten their understanding of roles and responsibilities as a contemporary mathematics instructor.
Broken Calculator Activity
Activity Andy and Mindy are assigned to be partners in math class and are to solve an equation. Mindy went to pick up their calculator back to their desks but dropped it, and by accident broke the 8 key. The equation that they have to solve is 9 X 68. Working with the person next to you, think of more than one way to solve this problem without using the 8 key. Explain your thinking in the space below using pictures, numbers and words. • Materials and Instructions •
Materials that can be provided for students are whiteboards to brainstorm answers, a set of math manipulatives to help students conceptualize different ways of reproducing and representing 8 for a portion of the activity. Students may work in small groups or with partners to discuss and share solutions.
The Broken Calculator This open ended activity developed by Sneha Gujadhura a fellow teacher candidate focused on developing individuals addition, subtraction and multiplication skills. This activity allowed for the exploration of diverse thinking as it did not require for a single answer to be produced instead it encouraged collaboration and independent work amongst pupils. Over the course of the weeks our aim has been to deconstruct what once was considered the “accepted” practise of mathematics instruction in order to provide better learning opportunities for both ourselves and students. Through the years there appears to be a flawed conception in that individuals have been reared to believe that there is only one way to come up with a solution when dealing with mathematics. Instead of prompting individual thought and growth students are instructed to follow a specific method to find a solution so that there is a universal answer. This undoubtedly proves to be problematic because what happens to those students who come up with a different way to solve a problem? Are they subject to unfair punishment and their voices left to be ignored? As an educator it is important to recognize the necessity of differentiated learning activities as all students process and retain information differently. In addition educators cannot expect that all students will learn in the same manner therefore we must become understanding and allow for the exploration of diverse thought to heighten student academic success. The “Broken Calculator” activity works to encourage academic progression as well allow for the exploration of knowledge and understanding through communication with peers and the process of trial and error. As a future educator I foresee myself incorporating an activity such as this one in my classroom for
Roll to Win! You and your friend are playing the most fun and exciting math board game ever, for the first time! You are so close to completing the board game, and lucky you! It is your turn to roll the dice! The question is tricky but you believe you are able to complete your task!
Roll each of the dice two times. Your first roll of the two dice will determine your first fraction. The second roll of the two dice determines your second fraction. Multiply your two fractions together in an attempt to get a whole number! Continue rolling until you get the whole number that you need to win the game. Don’t forget to show your work on either a piece of paper, a white board or the space provided below!
Once you have gotten your whole number…
That was a lucky roll, because you now have made it to the end of the game! You are so happy that you feel you must stand up and announce to the world “You have completed the most amazing math board game ever!”
Roll to Win! This fast thinking, high energy game, developed by Matthew Callaghan a fellow teacher candidate , aimed to strengthen students understanding and comfort level when dealing with fractional equations. Fractions is perhaps one of the more difficult units of study for both educators and students as they present numbers in an unfamiliar, unconventional manner. In addition, students are expected to add, subtract, multiply and divide these “odd” numbers together to create a “new” fraction, which I am sure you can imagine how complex and confusing it may be for a new learner. Even as a future educator, I continue to be uneasy and often perplexed when looking at different fraction equations. Our lessons regarding fractions focused on deconstructing the uneasiness felt as an educator when dealing with this unit of study in order to build the confidence and skill level to lead a lesson. As an educator we must acknowledge that like our students we will make a multitude of mistakes in our learning. We must realize that it is through our mistakes that we foster our growth as an educator. The learning activity, “Roll to Win” is one which encourages creative thought and the process of trail and error. Students are provided with a challenge however the activity does not rely on their ability to formulate an universal answer to progress. Instead the activity allows for diverse thinking and encourages continuous trail and error through independent and collaborative work. When completing this activity there appeared to be a high level of energy as students were excited to move forward. When educators promote students to become engaged in their learning they will heighten their likelihood to succeed. As a future educator I can see myself including an activity such as this one in my classroom for I feel that students will gain an adoration for it. As well, the activity can be modified and/or accommodated to fit a wide range of differentiated learning.
Joel's Kitten Problem
Joel’s Kitten Problem This classroom activity was perhaps one of the more memorable ones as it aimed to develop our understanding of ratios , rates and proportions through peer collaboration. This activity required individuals to begin by working together in groups of two to four to find a solution for the problem presented. As a group we were responsible to generate an answer through ongoing communication, which allows for a multitude of academic benefits. When students are given the opportunity to work with their fellow classmates they gage new ideas and techniques to creating a solution. Communication amongst peers becomes a vital skill to develop as a result, educators cannot discourage peer collaboration instead it should be intertwined within each lesson. When groups produced an answer we were required to explain, in explicit detail, our process of thinking and understanding. Once complete we joined together with a new group where we discussed our process of thinking. It was fascinating as well informative to have the opportunity to observe the multitude of ways in which the question could be answered. Although the method practised to generate the answer differed between groups, the final solution was cohesive. I thoroughly enjoyed participating in this exercise as listening, explaining and communicating with fellow peers not only strengthened my own 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. Students have the ability to become influential, knowledgeable figures however it is up to their educators to provide them with the required resources to grow. This lesson truly emphasized the importance of including peer team work to allow for a demonstration of understanding through communication. As an educator it is my responsibility to recognize effective classroom strategies so I am able to provide a nurturing learning environment for all.
Take it to the Bank This informative activity created by Nikolina Barisic, a fellow teacher candidate, aimed to construct an individuals apprehension and appreciation of the utilization of positive and negative numbers. What stood out most for me about this activity was Nikolina’s ability to relate the activity to a real life situation. The activity required students to make monetary transactions depending on the cards they were given out, at the end if the addition and subtraction was done correctly each table group member should have produced the same answer. To heighten a students academic development and ability to succeed educators must make the lesson and activity practical and relatable for students. When students understand that what they are learning is beneficial towards their everyday life they are more likely to succeed and become inspired to learn. In addition, when activities become relatable students are able to gain valuable morals and values. This activity was able to provide a simplistic example of how banking works and the consequences which follow when you take away more money than you have (you end up in the negatives). This activity was a great resource and one which I believe I will include in my classroom one day. Math effects all realms of our education and every day life and as educators we must aim to show pupils the benefits of pursuing math.
Mario’s Mirror Land This creative, skill enhancing activity created by Eva Chu a fellow teacher candidate reminded me of the fun which can be had while completing a mathematics assignment. Creativity is a skill which many individuals are blessed with however are often not permitted to pursue when studying mathematical equations. This activity allowed for creative expansion allowing for my level of enjoyment as well understanding of the concepts to significantly increase. Her activity focused on increasing students level of understanding of symmetrical figures while inspiring imaginative thought. The simplistic nature of the activity allowed for less emphasis on producing the “right” answer and more on the expansion of knowledge and understanding. As a future mathematics instructor it is my responsibility to create interest provoking activities and unlike past traditional methods of instruction I cannot present redundant complex questions which aim to challenge and evaluate a student’s level of knowledge. When educators do not work to build student’s foundation of knowledge there are depriving them of their opportunity to succeed and progress academically. Instead of aimlessly forcing useless information down their throats educators must take the time to investigate what works well within their learning environment. This activity demonstrates that fun and math can be included in the same sentence together however it is up to the instructor to allow this to happen.
25 Best Math Apps for Kids of All Ages
25 Best Math Apps for Kids of All Ages The twenty first century has transformed into an era dependent on technology due to the continued influx in social media outlets and devices being created. As a result, there has been considerable change in the practice in which individuals receive, interpret and utilize information available to them. For both students and educators to succeed in mathematics they must continually update their skill level and scope of knowledge. Digital progression and succession of students. As twenty first century educators we must take the time to discover and become familiar with different resources so they can be included in the classroom. The resource 25 Best Math Apps for Kids of All Ages presents and discusses numerous online databases and applications which can be explored by educators and students to help develop and strengthen their mathematic skills. The website explores a variety of educational mathematic activities for students ranging in preschool to middle school. The author provides users with a multitude of links and descriptions to numerous available resources which can be explored during classroom study or during leisure time at home. In my opinion this resource will become extremely beneficial within my field of study as I have recognized my greatest academic struggle is the understanding and developing of my skills and confidence levels in mathematics. As a student I had always struggled with mathematics and recognize that as an educator it is my responsibility to work at enhancing my understanding so that I can provide students with successful lessons. When students and educators are provided with the resources to assist with the development of knowledge and skill they have an increased opportunity of performing well academically. During my observational study I have noticed numerous teachers, including my associate teacher, explore different mathematics applications for they have recognized that mathematics is one of the subjects which has the greatest amount of student struggle. Students who have access to these applications appear a lot more eager and confident to learn as the activities are geared toward their field of interest. As an educator we must take the time to explore different applications for students as it will contribute to their ability to perform academically. As a contemporary instructor we must be willing to turn away from :�conventional� practises and instead look at ways in which we can provide the most inclusive, nurturing learning environment for all students.
Marshmallow Madness This skill building activity was created by Sabrina Girard a fellow teacher candidate. This activity was a marvellous demonstration of the importance of including visual and kinetic learning activities within a mathematics classroom to satisfy the needs of a multitude of learners. This activity was geared towards the development of understanding in regards to shapes, focusing primarily 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. One of the most important roles of an educator is to demonstrate to students why they are learning, how the knowledge they are imposing on them effect their every day lives. The activity was unlike any other we had explored as it required students to create a hypothesis and then confirm their speculation by physically constructing a figure. This type of activity bodes well for visual and/or kinetic learners as they are given the opportunity to question and/or verify their knowledge through physical manipulation. Through my years as a student I have observed that I am more a visual learner, I retain the most when information is being demonstrated to me through various images. As a result I thoroughly enjoyed the exploration and completion of this assignment as I was able to see the reasoning behind the solution. Educators cannot ignore the multitude of learners in a classroom, it is important that the needs of all learners are continually met so they have equal opportunity to succeed. As a future educator it is my responsibility that I develop activities which will satisfy the needs of all types of learners. I foresee myself incorporating an activity such as this one in future classroom activities for it truly expanded my knowledge and understanding of different spatial units.
Online Games
Online Games Over the course of the weeks we have explored a multitude of online games which aim to develop, improve and enhance a variety of mathematic concepts. Online stimulations have proven to increase a students ability to perform and develop academically as they allow for an expansion of knowledge and creativity. In my literature class I cam across an extremely resourceful and informative article titled “Video Games in the Classroom Building Skills in Literacy and Numeracy� the author prompts the idea of the incorporation of interactive video games and computer simulators in the contemporary classroom as studies have demonstrated that these outlets may be able to offer students interesting and informative context for learning. They hypothesize that the high tech graphics, sounds and motions allow participants to become active learners as they realize that their actions create a reaction allowing their level of interest to increase. The twenty first contemporary society has transformed into one dependent on technology thus educators must be willing to adapt these changes and introduce them into their classrooms to increase student success. When students feel as if they are being challenged their level of interest and motivation will likely increase therefore a game such as this one may aid in the development of individual growth and understanding of integer operations. Over the weeks I have had a chance to explore a multitude of games, some good and some bad, however it is so important that educators are taking the time to become informed of the available resources and include them in the classroom study for they can significantly enhance a students understanding of various concepts.
Number Tricks You are walking into the Burlington Mall when a disheveled man wearing a magician’s top hat approaches you. He asks “do you have any spare change, I’m an old magician who’s had some misfortunes lately and I just want a warm meal and coffee from Tim Horton’s.” You respond, “sorry…I don’t have any change.” You continue towards the entrance when he says loudly, “how ‘bout we make a bet? ”You turn around and face him, “what kind of bet?” you ask. “How about we do a math question and if I can correctly guess your response you buy me a warm meal?” You think to yourself for a second, and agree to this weird wager. He says to you: Pick any number, Add to it the number that comes after it (for example, if your number is 2. 2+3=5) Add 9, Divide by 2, Subtract the number you started with, He says to you, “Is the result 5?” Did he guess right? 2. Forwards/ Backwards Pick any number Double it Subtract 3 Double it again Add 2 Divide by 4 What number did you end up with? Now try the question in reverse. Select a number and work backwards. What did you do? What number did you get? 3. Any Number Think of any number Double the number Add 9 Subtract 3 Divide the result by 2 Subtract the number with the number first started with Compare you answers with your table Bonus: Write your own Number Trick on a whiteboard or in your notebook!
Number Tricks This thought provoking activity developed by Peter Jasinsky a fellow teacher candidate aims on enhancing students recognition of patterning and algebra skills, units which become integral towards a student’s overall success in their academic career. From a young age students are introduced to these concepts for they lay the foundation for problem solving and recognition of 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. An activity such as this one presents algebra in a non intimidating, “fun” way which may increase a students willingness to participate. Math cannot be presented in an intimidating, complex manner as it will significantly decrease a students level of interest. As educators we must be mindful when developing activities and ensure we allow our students to have fun while learning. I envision myself including an activity such as this one in my classroom as it allows students to realize that math is not intimidating and can allow for creative thought.
Guided Inquiry
Guided Inquiry •
This activity introduced us to the concept of the guided inquiry process demonstrating the academic benefits which follow when incorporated in the classroom. 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 by our professor, 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.
Frayer Model: Lesson Plan
Frayer Model: Lesson Plan
This activity was co-created by myself and my associate teacher Mrs. Leslie Gordon. This activity focused on developing students understanding of various mathematical concepts through independent and collaborative work. Through the course of the weeks we have been encouraged to go against conventional practises of teaching mathematics. We have been told to focus less on forcing students to learn and instead encourage learning so students become inspired to participate. This activity encompassed the “new wave� of mathematics as we focused less on teaching and more on exploration of knowledge. Students appeared to have a heightened sense of excitement, they were eager to share their voices and opinions. Math cannot be threatening and intimidating for students, as an educator we must
Assessment
Assessment 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. This lesson is one which will resonate with me as assessment will significantly contribute to my ability to be an effective mathematics instructor. My mathematics professor did a fantastic job laying the foundation to my understanding of what it takes to be a great mathematics instructor. I will take these lessons and activities and use them to my benefit.