Class 7: Personal Reflection - Week of October 27-31, 2015

Personal Reflection - Week of October 27- October 31, 2015

        Class began with a visit to the Bedtime Math website. We were encouraged to do the Pumpkin Face Off! Activity. 

http://bedtimemath.org/fun-math-pumpkin-carving/

This served as a good site for introducing technology night to us. I had not seen Bedtime Math before. It would be a great site to use with elementary students in the classroom, because each day there is a new problem provided. One aspect that I did not like is that the author divides the children by wee ones, little kids, and big kids. If an older child were struggling with Math, he or she might be only able to to complete the wee ones problems. This may make them feel alack of confidence in themselves. Perhaps the problems could be worded differently, so they could be more inconclusive. I also took the opportunity to look up the books on amazon. The books would be engaging for children and parents.  According to Amazon, the book in the series that I looked at is aimed towards 3-7 year olds, but I believe the books can be extended to children that are slightly older.  This may also serve as a helpful resource book for older children as they work on acquiring Math skills.

Bedtime Math can be found at Barnes and Noble. 

http://www.barnesandnoble.com/reviews/bedtime-math-laura-overdeck/1122518873?ean=9781250035851

        We also had the opportunity to visit the AVRSB Learning Portal.  I was most interested in looking up the various Mathematics rubrics, because this is an area that I was interested in seeking further information. Some of the rubrics that I looked at included the problem solving and communication rubric, How close to the target are you?, and Math interview questions as well as others. My favourite was the Math Interview Questions, because that gives a teacher of a student’s attitude towards what they are currently doing in Math, the process they use, and also the end products. Plus, there was plenty of space to write longer comments. It was helpful to be able to visit this site to gain a better understanding of the resources that will be available to us as teachers.

         We were told about the Math Dictionary for Kids. If we do not understand a concept it would be helpful to review the terminology involved through using this dictionary. Plus, this will be a good resource for our future students to use.

         Out of the websites that we had the opportunity to visit, my favourite was illuminations. The games were interesting.  I enjoyed played Turtle Pond which involved estimation and angle measurement, Pan Balance shapes was engaging, Horizontal Additional used the number line, Bingo was another fun choice. I played Bingo - Addition and Bing – Angles.  The Gingerbread game could be linked to a gingerbread story that could be extended to Language Arts. 

        During my practicum, last spring, the children were sometimes allowed to play educational games on the computer that were Math based. I always found that the children enjoyed the games, and through having fun with Math they gained a greater appreciation for using Math during their regular routine Math lessons.  Technology certainly can play a positive role in encouraging learning.

        Virtual Manipulatives is arranged according to grade levels: preK-2, 3-5, 6-8, and 9-12. This is a resourceful site containing tools such as base blocks, bar chart, circle 99, and many others. This could site could be used to supplement Math or perhaps incorporated directly into a Math lesson.

      Thinking Blocks is another outstanding site. One game that would be fun for children to play is the Money Game. The children are able to use a hammer to break the money down.

       During our class, I enjoyed learning about incorporating technology in Math. This is a task that I will certainly take on in my classroom. The students enjoy using computers to play games. They also enjoy the Smartboard. On the downside, some schools are not as equipped as others, but this should improve in the future provided better funding or with the help of fundraisers.

         The Tumblebooks site is another that is exceptional for use in Resource or in the classroom.  I have used this site to help children that are struggling with reading. I’m also impressed with the amount of Math based books.  At home, I watched and listened to the book, My Odd Day by Doris Fisher.

This is an excellent book for children in grades primary-to-three, but can also be used with older children. The author teaches the concept of odd through her story making it fun for children to learn what odd is all about! Plus, she follows up in another book with a story about even. 

Class 7: Chapter Reflection – Week October 27-31, 2015

Chapter 4: Helping Children Master The Basic Facts

        This chapter covered a great deal of information. However, I found the most important, especially for me as a student teacher is that it educates us to not only get children involved in learning Math facts, but teaches us the importance of allowing children to develop their own Math strategies. While the author reminds us that knowing Math facts is necessary, knowing the facts alone does not mean that a child has a good grasp on the material. I think it’s also meaningful to remind us that we should not simply be passing our own strategies on, but encouraging the children to learn their own way of solving problems, because there are so many different ways that Math can be done. We each learn in our own unique way how to problem solve. It can be tempting for us to drill students, but we must ensure that they have a strong understanding of their Math before doing drills. I also felt, that the authors gave a positive suggestive about the role of introducing individualized drills allowing the student to use the strategy they had learned.

       

      The chapter contained a vast array of activities that would be useful especially for new teachers, because we have so much to learn about using games, activities, and techniques that encourage children to enjoy learning. I was surprised that subtraction tends to be more difficult for children to learn than addition. Therefore, I would be more likely to spend greater time on connecting subtraction to addition. Learning this, I would also spend greater time on activities that more effectively help children learn subtraction such as “Build up through the ten frame” and “back through ten frame activities. “ Likewise, I feel that all the activities would be of use in the classroom. I would certainly incorporate all as I was teaching the various Mathematics units, but also first ensure that my children understood their own Math strategies including how to solve word problems.

      Lastly, I found this video on youtube.

 We often think of teaching the children alone, but I believe creating videos that parents can also learn from and use to help their children with homework can be incorporated. This helps parents to understand the newer methods of Math. If the Mom or Dad were feeling excluded such videos may put them at ease, and help them to feel they included in their child’s learning process.

Personal Reflection (October 20-to-24, 2015)

          During our weekly math class I learned two new terms, “commutative property and “distributive property.”   According to the commutative property two numbers can be multiplied together and the distributive property a single term and two or more terms that are in brackets also known as parentheses may be multiplied together.

      The information provided during the problem solving lessons was helpful to us, because one day we are going to need to be modelling problem solving strategies for our students. We need to consider all the ways that problems can be solved. I especially found the Problem Solving (PS) sheet to be useful. One of my favourite quotes from the sheet is, “Problem solving is also a powerful teaching tool that fosters multiple creative, and innovative solutions.” This makes future teachers think of the importance of incorporating Math into other subjects, because the depth of Math will also be beneficial for solving problems in arise in Science, and in other subjects.

      It was interesting to observe different techniques for solving the same Math question.  Showing how children can pictorially use groups to represent a Math is meaningful to future elementary teachers, because we need to be exposed to a range of ways that children can do their work and explain their work to us.  For example our group enjoyed, “The Puddle Problem.” We came up with many ways to solve the problem through using string to measure the perimeter, using footsteps, collecting water in a measuring cup to predict how deep it is, and measuring depth with a ruler. I also found the problem-solving menu to be incredible! I would not have thought about fourteen ways that problems can be solved!

Integrated Curriculum Reflection (October 20-to-24, 2015)

        My impressions of the children’s book, “Grandma Lena’s Big Ol’ Turnip,” is that the storyline would appeal to both children and adults.  The pictures in the book are colourful.  Repetitive phrases make the story more interesting to young children, and are also patterns.  The humour pulls the children in without them realizing that they are learning.  Adults and children alike would laugh about the giant turnip and the number of people required to pull it out of the ground! 

                                 

        The book is cross-curricular for covering a range of subjects. Social Studies is included, children learn about southern culture and foods, and about the importance of community. This story can be used in Language Arts. Science is covered, children can be taught about how seeds grow into plants. Kindness is also modeled throughout the story with Grandma Lena’s family and community coming together to help her, and in turn she prepares some delicious meals to feed them.

        Math is represented in many ways. Children do not realize that they are enjoying reading about problem solving, how to pull a giant turnip from the garden,  and counting is also covered. It took five people (four adults, one baby), and one dog to finally pull out the giant turnip. This covers the SCO NO3, students will be expected to relate a numeral 1-to-10 to it’s respective quality.  The five people and dog pulling out the turnip helps to meet the performance indicator for N03.O1, name the number for a given set of objects. Children can also use a counter to represent the number of people or in this case objects. Blocks would be helpful.

        Given the artwork showing the number of people pulling out the turnip, the performance indicator, N03.02  match the numerals with their given pictorial representations is met. Children can draw the number of people and the dog that helped. They can also represent grandma’s dishes through drawing pictures. The seeds can also be presented by drawing a picture. The children can also count the seeds and growing plants.  Performance indicator N03.03 can be met by asking the children to hold up the appropriate number of fingers for a given numeral.

        Lastly, the story also leaves children with a positive message from Grandma Lena. “Anything worth doing is worth doing right. “ 

       

Grade Level Performance Indicators: Grade Primary 

SCO

PNO3 Students will be expected to relate a numeral 1-to-10, to its respective quality.

Performance Indicators

PNO3.01 Name the number for a given set of objects.

PN03.02 Match the numerals with their given pictorial representations.

PN03.03 Hold up the appropriate number of fingers for a given numeral.

Class Reflection: Workshop Model in Math Class for the week of October 6, 2015

      Reflecting back to my childhood, I believe too often that Math appeared dull. A quick lecture model, and worksheets were responsible for many of my Elementary Math days.  However, I do still recall playing Around the World game in the fifth grade. Often, if our teacher had some additional time to spare, he would allow our class to play this game. We were rewarded with sticker. The competition for stickers was an added motivation, but the game on in it’s own respect made learning much more fun.  The entire class always enjoyed playing the game.

        What I have seen thus far when completing my practicums supports my contention that learning should be open to a diversity of resources. Educational games should be amongst the teaching toolbox.  A child’s learning process tends to be much more engaging when learning is hands on. This would include when working with a small group or a partner to include a game.  I have seen shy students light up with excitement not only about the game, but also about learning a new rule or how to add and subtract when using a simple manipulative such as dice.  Many games can be adaptable to help children that may have a learning difference. For example, by pairing students that may require greater assistance with the teacher, EA or other students and also by modifying the game rules. Often some competition can be a motivator as long as fun is involved for the class.

          While many children do enjoy playing Math games, having a class that is a workshop model may also present a challenge for students that are less confident in their Math skills. These students may require prompting by their teacher or perhaps may want to work with others in their group. A student experiencing some difficulties may prefer to not be the presenter for the group. Perhaps, a stronger Math student can be assigned this task. In my own experience, The Millionaire Game was enjoyable, but a bit of a challenge since I did not have the benefit of having done place value in a number of years.  

 So, I certainly do think of children that struggle with Math. It would be anxiety provoking for them to be playing this game with their peers. This may also lead to behaviours by some children, such as pencil sharpening, and so on to waste time. Therefore, I can well understand how these games may present some anxiety to children. I believe that teachers have a role to teach the children that we all learn differently. Some people may struggle more with some courses than others, but all children and adults have a valuable role to contribute in the classroom, and in the community. We need to be aware of signs for those children who are facing difficulties.

         My group did not have the opportunity to finish all the games. If I were to do a workshop model with my own class, I would have fewer games or operate over the course of a few days or week.  Certainly, I would embrace this teaching model. The Place Value game was among my favourites.

        Overall, I enjoyed learning about the various kinds of Math games, I feel that by making Math an exciting subject to learn when a child is young, that just as many students also acquire a joy for literature; that they are more likely to develop a love for learning math. Math games can also increase student’s critical thinking skills that will help them to become more logical, independent thinkers. I also believe in the value of teaching children chess to help them to develop their creativity and logical thinking skills, as they grow older, and also in the possibilities of including music and math together in someway. Both are linked to helping children engage in and develop skills that will further help them in STEM based courses throughout their educational careers.

         

Late Number Sense: Personal Reflections (Week of September 29, 2015)

 Late Number Sense

 While You Wait Activity - Number Line for Estimation

          When coming into class, I found that my table was already engaged in deciphering numbers to be placed on a number line. It was interesting, because we were to represent numbers from A B C D E. The only number that had been provided was 200. This caused much thinking as well as class discussion as we all sought to estimate what should be the starting number for the number line, and where the other numbers should fall.  I think that this would be an excellent activity to use in the elementary classroom with students in grade three-to-six, possibly upper middle school grades  could also use this as a review.  Trying to determine which number should come next in the line was certainly stimulating.

SMARTBoard Hundreds Chart

        The use of the SMARTBoard when reviewing our homework for the Hundreds Chart was very helpful. This activity promoted much class participation. It was useful in learning how others thought differently. There were many ways of coming up with solutions for our problems such as counting by: twos, fours, threes or circling all the twos. One of my classmates circled eleven along with all numbers corresponding with the number eleven. What I appreciated about this activity was that it was engaging and would allow elementary students to discover that there are many solutions that one can use to develop Mathematical Patterns.

Connections 

        We read about the importance of connecting ideas in Math to our daily lives. I think this is important to teach children from an early age. When children learn that Math is literally everywhere this may help them to understand the importance of Math in their daily lives. For example, a child may be taught a recipe that he or she will be able to cook for their family. A child can also use Math to measure when cutting material or paper for a craft. Children can also be taught to see connections in Math in road work, bridges, banking, medicine, and so on. Such connections build a child's understanding much more than simply telling them to complete their Math work. Connections make learning fun!

How Many Seeds in a pumpkin?

        We spoke again about the story, "How many seeds in a pumpkin?" The idea of how children can estimate is helpful for them to learn when a number needs not be exact. This book was also important, because it teaches children that size does not always matter.

          Our group also had the chance to estimate various referents. One strategy was to place a hand over the objects to make a guess. Another was to guess by dividing up the various piles of animals, counters and foam shapes.  I learned that differentiation can be done by in some of the piles using lower numbers.

In the case of the animals my group's estimate was 25, but some other estimations by my classmates were 40, 45, 44, and 30.

For the foam shapes our group's estimate was 120. Other groups choose their estimation to be 100, 120, 150 and 160.

 Estimation using counters were also done.  The counters were trickier to estimate since there appeared to be so many of them. Our group guessed that there were 280 counters on this table. Other estimations from various groups were 140, 180, 220, and 258.

Levels of Place Values

        This is an important topic because, when we observe children working in groups it can appear that a child has a greater understanding of the topic than he or she actually does.  However, the child may not fully grasp what we are trying to teach them. I found the information provided about single numerals to be helpful.  As adult learners we have have a tendency to think that children would see numbers as we understand them, but a young child may only view a number such as 16 as a single number rather than the 1 and 6. It was also compelling to learn about how children view position names, face value, and transition to place value. 

Racing Game

     The racing games were interesting and fun. Most importantly these games help to build on the skills we have been teaching the children.

Numeration Principles 

      As future teachers it will be important for us to understand where a child is struggling. We need to recall, the purpose of zero which is to hold the place value, so we can properly educate our students. Furthermore as adults sometimes we overlook what we understand. We always need to keep in mind the children's neurodevelopmental levels and skills which correlate with their cognition and understanding of concepts. I felt this area of the lesson was important. We all have a tendency to say a number incorrectly. We must model the proper way for our students in order to build their understanding. For example, stating "321 is three hundred twenty-one," without the and which is to be reserved for decimals.  I will need to remind myself not to add "and" to the hundreds and thousands!

Manipulatives Used ... Only Base Ten?

      It is surprising to learn how many different types of manipulatives can be used in teaching Math.  Manipulatives that I will find helpful in using with the children include open number line, closed number line, flats and rods, popsicle sticks, money and change.  Importantly, larger numbers may be represented through using a base ten block. I was also taught in class that base ten blocks can be used to represent decimals.

Amanda Beans Amazing Dream

       I enjoyed hearing this story about a little girl that loved to count.  By the end of the book Amanda was taught that mutiplication can help her count more quickly than counting on it's own. This would be a fun and educational book for children in grades primary-through-grade three.

Chapter Reflections (September 27-October 3, 2015)

  Chapter 5:  A Focus on Problem Solving

        This chapter provided valuable insight into the importance of children learning problem solving.  When I was attending school, as previously mentioned, much of my early Math involved sheet work, which was often repetitive. I strongly suspect this is one reason that early deprivation in problem solving skills caused lead to Math to being a struggle, but one that I’m working to overcome!

      The author did a profound job in discussing her reasoning about the value of problem solving. Teaching children to be able to work independently and with others to become skilled problem solvers will help them develop critical thinking and judgement skills.  

         The inquiry process is intriguing, because it involves crucial stages. The first being able to understand the problem, and the last being able to look back at the process. Looking back is a crucial stage, because the students are able to share their problem solving skills with each other.   

        I had never seen a graphic organizer used in Math and feel this would help students in their inquiry based learning. It would especially be helpful in brainstorming and during other activities.

       The explanation and examples provided for the creation of good problems was a beneficial reminder that as teachers we want our students to try different ideas. We must be open to multiple ways of problem solving allowing the children to experience growth through their learning.  The array of both simple and complex problem solving strategies is astounding!  I found the examples to be a helpful review and preparation for myself before attending the fall practicum.

Chapter 5 Problem

"Ian has 75 cents in quarters, dimes, and nickles. He has at least one of each type of coin. How many coins could he have?"

         When doing this problem, I choose to use money, because this is one way that a child can represent this problem.  Personally, using change made it easier to break down the various ways of to discover how many coins Ian could have.  My cooperating teacher had fake coins that she allowed the children to use as a manipulative when solving similar problems in Math.

 

Chapter 8: Developing Early Operational Concepts

        This chapter was filled with detailed information.  Most importantly, what I took away were the similarities between addition, subtraction, multiplication, and division.  Subtraction seems like a straightforward operation, but when compared to Addition the complexity including the terminology was surprising. For example, separation of items is involved in taking away, comparing a larger number of items such as 7 cookies minus 4 uses subtraction, and also that determining a larger number from the smaller to find the addend is sometimes

necessary. 

        The chart for the addition and subtraction principles is helpful in breaking down information. From a teaching standpoint this improves our understanding, so that we can better teach the children. Principle six involves adding or subtracting six from a number. An example provided involved having the students walk on a number line. This would be a fun way for children to learn this concept.

       

        In reading this chapter, I learned how manipulatives such as counters, game materials (such as dice), linking cubes, 10-frames and walking on the number line are all helpful when teaching children about addition or subtraction. It was beneficial for me to learn that linked cubes, game materials such as cards, and number lines have a role in teaching multiplication. This opens the door to learning in so many ways beyond memorizing tables.

        What I did find rather cumbersome was the depth involved in the multiplication and division principles, because, I had just covered addition and subtraction principles.  Simply, this informative chapter contains an abundance of information to muster.