Sunday, 27 September 2015

Personal Reflection ... (September 22, 2015 - Class)



Math Game

      Upon arrival to Tuesday’s class, I was surprised to learn that my classmates and I were to play a game that would allow our classmates to learn more about our learning styles. For example, I’m a hands on and visual learner, these were also two of the choices on our paper. The activity was excellent, because we were able to have a short meet and greet with our classmates. This was helpful, because, I’m still learning names. By doing this activity we also had to think about our own learning styles. In the classroom as an elementary teacher it is important that we know as much about our student’s learning needs as possible.  As a teacher, I may consider doing an activity such as this one in my class, because it can also help the students learn more about themselves.

Shifts in Learning Math

        The shift that has occurred in the way that Math is being taught in the classroom makes Math more meaningful for students. Manipulatives and games create a classroom that is invokes creative learning. I feel that the way that Math is being taught in these classrooms makes it compelling and fun for young learners.

        As a child, my teachers at school used to review the multiplication table with us. I also remember my parents doing the same. Although, I’m not fully convinced that removing the tables has been necessary; I do believe that some of the changes that have taken place will lead to children having much more positive experiences in their learning.  

        I still recall doing Math sheets throughout elementary school. One day, my second-grade teacher even rapped my fingers with her pencil; I had been speaking with a friend when we were supposed to be doing our math sheets! I never forgot getting in trouble, but do not recall enjoying Math in Elementary. It would have been much more meaningful to be able learn Math in a much more creative way. For teachers, surely this also makes their teaching much more compelling.

        When I was a child, the teacher would sometimes mark my answer incorrect even if the answer were correct. We were often taught that there was only one way to solve a problem as opposed to there being multiple solutions.  Allowing for children to explore different ways of doing Math strengthens creativity.  I believe this also may lead children to embrace both Math and Sciences. As long as the child can provide their answer and explain how he or she came up with the solution different pathways should be encouraged rather than stifled. 
 
Gradual Release of Responsibility

        Jill also reviewed the four parts of the gradual release of responsibility with us.
As teachers we will need to follow these steps:

1.  Model it
2. Teacher works with children
3. Children work in a group
4. Children work on their own.

During my practicum, last spring, my cooperating teacher taught me these steps. The hard part is stepping back, because I always want to be able to help the students. However, I also realize that by allowing for gradual release students are learning through working with one another. They also develop a sense of pride in their work along with independence. 

 
How Many Feet In The Bed: Lesson Plan

       Our group spoke about the book, “How Many Feet In The Bed.”  We used manipulatives to represent how many feet were in the bed. The group work made me think of the importance of integrating Math related stories into one’s classroom.

This is our representation for the pattern – how many feet?




I also took several photos of work done by other groups.





Lessons involving stories that include Math are important. They allow a teacher to include more than one subject. Different cross-curricular outcomes can be met. For the students creative and critical thinking is involved. They must as a group come up with their own way to represent story. Therefore, problem solving is also being taught at an early age that a child will build on throughout his or her schooling.

 
Taking Inventory …

        This task involved all of our group members to imagine how the keys can be represented.



Since there is a small number, a pictorial representation may work. However, Jill warned me that this would not work when it came to representing larger numbers of objects. At our table, the group brainstormed about multiple ways of representing the keys. Someone also suggested counting by ones and twos. Since time was limited it was difficult to think clearly on the spot. Counters and craft bundles could have been used, because they also represent small and large samples.
 

Skip Counting

      Skip counting is something that I do recall from school. It can be an interesting Math activity for children. They are learning to use numbers other than one to move backwards or forwards. I believe this kind of Math activity can appeal to many students. They may perceive skip counting as a game, plus they are learning to count more quickly. 



 
Math Language: Comparative Language

        Tuesday’s class brought home the importance of being clear in our language. Otherwise miscommunication can be the result. I had not realized that the term “more” could lead to confusion among young students. It was surprising that word choice can make such a difference. Instead of using the word “more” we were taught that “greater” should be used. Until the children are older, and using greater and less than symbols, we can for example state: 3 is greater than 2. This will certainly be helpful for me to recall when doing my teaching practicum.

A Sense of Number

        The number charts appear to be easy to follow. It surprised me that I did not find this exercise to be as easy as I thought that it would be. When teaching number lines to children we need to be just as patient with them or more so than we are with ourselves. 


 
Video: Good Morning Ms Toliver

                                 
                                                             (Full Video)


       The take home message from watching Ms.Toliver teach was to have a sense of confidence in our abilities in a teacher. She is amazing teaching, because Ms.Toliver is carries an abundance of enthusiasm both for her students and also for her subject area. She believes in the children. By believing in them, she is teaching them to believe in themselves. I had never seen Math addressed in such creative and fun ways!  She teaches children, not only is Math fun to learn, but also really all learning can be interesting, as well as challenging. Although, Ms.Toliver is a Math teacher she incorporates some writing into her course. Thereby, her teaching incorporated Language Arts. I also thought it was fantastic that she took her students outside the classroom for them to study, and she that Math is everywhere from buildings, to bridge designs, and even how many kids can sit on a bench.

 
How Many Seeds in a Pumpkin by Margaret McNamara



        This book would be helpful in teaching skip counting and estimation to children. When reading the book to a class a teacher can also stop at various parts and ask for the child to predict how many seeds they think the smaller and larger pumpkins will contain.  There is also a lesson about smallest to largest. Children learn that being the smallest is not always so bad.
        It would a good book to introduce in the fall close to Thanksgiving to provide integration of Language Arts and Math.






Friday, 25 September 2015

Chapter 9: Extending a Sense of Quantity with Larger Whole Numbers


       Although, I had been a school volunteer and have completed two practicums, receiving an explanation for grouping was helpful to increase my understanding of this practice.  The diagram explaining why grouping is done, and how it can help students opened my eyes to the larger picture. Now, I can certainly understand that grouping is helps students have a better concept of whole numbers. 

      The numeration principles section was well outlined. I especially appreciated the summary pertaining to the five numeration principles found on page 195.  The brief summary was helpful in rejuvenated my memory after reading the longer passages. Diagrams provided in addition to the readings, such as the 10-frame and unifix cube stacks were also beneficial in gaining a greater understanding of the principles. Indeed, all the diagrams provided with the five principles helped one to come away with a better understanding of how using similar tools such as craft sticks, counters, a hundreds chart and other manipulative used during Math can help us to provide greater insight that will improve our students’ understanding of these concepts. 

        I was pleased to read the section pertaining to common errors and misconceptions. Examples and strategies given would be especially helpful for new teachers. For example, how we can help children learn about 0? It had not occurred to me that 0 being included in a number such as 304 can be difficult for a young child to grasp. 

        Lastly, including the children’s book section serves as a reminder that we should incorporate Math into Language Arts, and other subjects.

Saturday, 19 September 2015

Article: Developing "Five-ness" in Kindergarten


              Janice Novakowski’s article pertains to children’s ability to understand 
at their own developmental level how a certain number of objects, in this case five can be representing in a number of different ways. The role of five including being able to count to five is essential in order for the children to understand how to count to ten.  In order to help children learn what five means they are given many ways to represent five from drawing to building blocks to using Popsicle sticks to create designs involving five. Children can also be asked to pretend that that have five objects, and to draw or craft them in a certain way. If they do not grasp this understanding a teacher can provide further examples.

               One of the activities that I thought was helpful in demonstrating number sense to the children came from a reading and arts activity. They were read, Ten Black Dots and afterwards created artwork around five black dots that had been placed on a sheet of paper. This allowed them to use their imaginations.  One child drew a snowman and another a house. Using literature in a meaningful way allows for number sense to be more likely to be understandable, as well as memorable for young children.  Learning is made fun rather than being a chore.

How Many Feet in The Bed?, September, 15, 2015, Class #2



       Near the end of the second class, Jill read, How Many Feet In The Bed? This book teaches children about counting in a fun way. In class, a teacher can read this book to his or her class. Afterwards the children can represent how many feet through drawing, making charts showing their counting work or through addition. Since there are many ways to represent the answers children should be encouraged to choose their own method to solve the problem.

Class Notes, September 15, 2015

Can you arrange the blocks in a different way?  

 When reflecting back to our class, I feel that this activity is important in demonstrating
to children that although the arrangements of the blocks may change the number of objects stays constant. However, some children may not yet understand that the arrangements are only changing. In this case, they may have trouble understanding even when asked to explain the groupings. As teachers we need to be observant, yet knowing that developmentally this will come for most children. If they are still struggling it is time to intervene with resource help.



An activity that allows children to work with blocks or another counter makes learning interesting for children. They may view this as play not realizing that they are learning.  Teachers can discover if an individual child or other children in the class understand counting. Do they understand why the number of groupings hasn't changed the amount of blocks or other objects within the group?

This activity is important in promoting the Mathematical processes of communication, problem solving, connections, visualization, and reasoning. Hands on activities help children learn, because they are physically able to manipulate an object. What a teacher is looking for is for the child to be able to reason their way through their math problem, and to explain the math. If a child is able to do this he or she understands Math.  If children do not understand it becomes important to tweak the lesson or work with them individually until they do understand.

Differentiation was addressed in class. I agree that we can help young children by continuing to ask them lots of questions, and keeping them engaged in the learning process. Too often when children experience difficulties they may feel like giving up, but we must not give up on them.  We can help our students by making adjustments. Unless a child has a global delay placing him or her on an IPP will hinder rather help. As teachers our goal should be to help every child meet learning expectations to the best of his or her and our own capabilities.

Communication
Allows children to learn to express their understanding of mathematics. Oral communication can take place with a student or small group, teacher or whole class, peer talk, and self talk.

Written Communication can involve a students personal writing, descriptive writing, process writing, and creation of words or problems.

Symbolic or Graphic Communication is more visual, including mapping concepts.

As children are taught all forms of communication they are better able to retain the concepts they have been learning. Since we all have a different learning style, visual communication maybe more helpful for some students whereas other children learn better through being able to communicate orally.

From my perspective as a student teacher, I believe that written communication is important, because it will allow me to integrate Math into a Language Arts lesson or into other lessons such as Social Studies.

Bean Thirteen


              During the first class, Amy introduced the children's story, Bean Thirteen. The main characters in this story are Ralph and Flora, two insects that enjoy eating beans. Close to supper, Flora discovers that she has 13 beans. Poor Ralph is upset by this unlucky number. There has to be a way to change their plight!



            The story is entertaining for all ages! However, young children have fun learning math without knowing that they are being taught about division, grouping, and prime numbers. This book would be helpful for grade two, because children are being taught many of these tasks through the second grade curriculum. However, it would not be a selection for a grade primary Math lesson since the primary students only learn their numbers up to ten. The book can also act as an introduction to even and odd numbers that are introduced in grade two.  Bean Thirteen can be an opener to discussing the number thirteen. As adults we taken for granted that some children may not yet understand why some people believe thirteen to be an unlucky number.


           Bean Thirteen allows for a teacher to incorporate both Language Arts and Math together. He or she can help activate literacy and math connections. One possible question to ask the children, do they think the ending is fair?


           

Pre-Class Math Activity: Pentomino Puzzle


                                     This activity was challenging. The reason I would have my
                                   future class piece together a pentomino puzzle is because this
                                   learning challenge would be fun and engaging for my students.
                                   Perhaps, the puzzle could be made less complicated depending
                                   the age group. This could be a good end of the day activity or
                                   could be completed by students if they complete their Math
                                   early.  Teachers can allow for differentiate by allowing children
                                   to work in pairs or small groups.
                           
                                       
                                       
                                   
                                                         The answer key for the puzzle.

A typical child on Piaget's conservation tasks

Chapter 7: Mathematics for the Younger Learner


     
      By the time a child starts grade primary he or she has already learned an astonishing amount of information. When thinking of the little ones starting school, I cannot help but wonder that they will soon be learning rote numbers. However, some children still have difficulty counting. They may skip over a number or leave some out entirely. As teachers we have great expectations for our young students. It is important that our children are not left out when we differentiate.

       For little ones in the pre-operational stage of thinking, four-to-five year-olds do not yet fully understand conversion – that something remains unchanged. Gradually from seven-to-eleven they began to have a greater grasp on learning Math. This stage is also known as the concrete operation stage of Piaget’s model.  As teachers we must be patient, and understanding with Elementary children.

      When further reflecting on this chapter, counting also caught my attention. Counting is complex for involving counting forward, backward, counting on, and skip counting. If a child misunderstands a counting concept, I can certainly envision that this would be a source of frustration.  Helping struggling students as early as possible is essential for their understanding and learning.

        Number representation was well demonstrated. There were many examples shown such as numerical, pictorial, 5-frame, 10-frame and others that are helpful for teachers.  These examples are a learning tool helping me to gain confidence grasping the Math that will one day be taught to my students.

        Overall, I found this chapter beneficial due to the array of information provided.

Friday, 18 September 2015

Chapter 7: Chapter Problem


       
      I would use a task similar to the chapter problem when teaching students
differences between numbers.  It could be used to teach students about the variations within numbers.  Before Math started, I would lead a class discussion to determine what the children may or may not understand.

       In this type of activity children are learning how to describe different sets and characteristics involving numbers. I feel that this kind of work may work best with pairing or small groups. Children tend to learn much from one another as they collaborate with careful observation and guidance from their classroom teacher. Plus, allowing them to use manipulatives such as various counters, geometric shapes, and also their own drawings can help them to answer these kinds of questions that do involve critical thinking.

        This form of problem solving addresses greater and lesser numbers. Gradually, students are being taught about groupings, rows, and geometric shapes and differences, division, and subtraction.  The lesson can be cross-curricular involving either the same numbers or others. Through Language Arts, stories that are both educational and entertaining can for example teach counting to children. The book should be inconclusive for the children’s grade level in order to meet the curriculum standards. Therefore, it is likely that in my classroom that this type of Mathematics lesson would be used fairly frequently, however, the chapter problem appears to be more adapted to middle and upper elementary as opposed to grades primary-to-two.  For lower elementary, it could be adapted to meet their learning needs and outcomes.  

Pre-Class Math Assignment




Please tell us a little about yourself...
HOME
The Annapolis Valley has always been my home. I was brought up in the community of Hillaton located near Canning. Now, I live near Wolfville.
DEGREE(s)/Universities
In the October, 2000, I graduated with a Honours in Sociology and a Minor in Psychology.
Last year, I started my Education degree at Mount Saint Vincent University, transferring for the winter term, and for the remainder of this program to Acadia University.
FAMILY
My Mother had taught school with a permissive license when she was only 16 or 17-years-old. She was a teacher at schoolhouses in Scott’s Bay and Blomidon. Often when shopping some of her former students would approach her to thank my Mother. She was always interested in their lives, and eager to learn about their families, and experiences. Mom was proud of all her students. Unfortunately, we lost her May 1, 2011 due to Alzheimer’s and Parkinson’s-related dementias.
Dad spent his working life as a farmer. His farm consisted of raising livestock, as well as growing fruit, and vegetables. He later sold the farm, and became a stationary engineer for the Graves Plant which became Cobi Foods, and has since become Oxford foods.
I have two older brothers. My brother Arthur lives in California. He has two young adult daughters, and a one-year-old adorable grandson. My brother, Paul lives with his wife, and children on the South Shore.
Family time is precious; I always enjoy spending time whenever possible with my loved ones.
INTERESTS
My interests include: Learning differences, reading, movies, learning violin (especially classical violin), arts and crafts, Crokinole, playing board games, puzzles, and movies.
STRENGTHS you will bring to the math classroom
Math has always been a difficult subject for me, but I will always strive to do my best, and never give up, especially when helping a child. I would like to make the lessons fun, creative, engaging, and integrate games whenever possible. Our science professor, Mr. Gregory McKinnon also spoke to us about the use of technology in the classroom. I would also appreciate learning how to teach Math using Smart board programs.
CONCERNS you may have about teaching math
As a mature student, until last year, I have been absent from the classroom for a number of years minus my volunteer work at various schools. Math has always been a challenging subject. I do worry about making mistakes that could further confuse my future students.
ANYTHING ELSE you think we should know about you
I have a significant respiratory disease requiring treatment by my Respirologist. My illness is treated like a form of atypical cystic fibrosis (CF). This means by times that I require IV antibiotics. Often my IVs can be given at home. Sometimes, it’s necessary for me to be admitted to the hospital for a few days to receive IVs and aggressive chest physiotherapy. The VON also has a busy schedule. By times, I may need to miss a class or part of a class if they cannot work around my school schedule. However, despite these challenges I always work hard to stay on top of my classwork.
QUESTIONS that you might have for us
Will there be a time that we can receive extra help if necessary? In this course, will there be a lot of group work?

Saturday, 12 September 2015

First Course Reflection Notes from September 8th's Class


Chapter 4 Problem Reflection

        Thinking of the problem as a game similar to Scramble inspired me to piece the puzzle together leading to solutions.  Brain storming also took place in hopes of more quickly finding answers.

        The use of the Alphabet is cross-curricular since this includes not only Math but Language arts.  However, it took me about a half-hour to find three words that added up to forty-three. In hindsight this was not a very efficient way to solve the problem. Fortunately, there are other means to come up with solutions. 

        Differentiation can be and should always be taking place in the classroom.  As previously noted allowing for differentiation when creating until and lesson plans, and certainly in our daily teaching, reaches children that may have otherwise tuned out.

         Visual learners may prefer to use a number line. Some students may use rods and base units to help formulate answers. Other children may find counters helpful.  Positive whole numbers and negative integers can be utilised.  Children maybe allowed to work in larger groups, with their teacher directing learning, or with a partner to solve the problem.


Course Reflection Images, September 8th Class


                                          Chapter 4 Problem


Friday, 11 September 2015

In my first, Elementary Math class, my partner, and I demonstrated how rods can be used to help children understand adding. In this case, adding up to 100. In Mathematics the use of such tools as rods are known as manipulatives.







Chapter 4: Planning Instruction


  Chapter 4: Planning Instruction

      Math Anxiety is a fear that many students and teachers alike have experienced. The challenge will be helping our students to have a positive experience with Math. Through the use of games such as Around the World, and also providing positive help, and feedback we may better help our students, so that Math anxiety does not limit their career choices. As teachers we must not be too hard on ourselves when striving to overcome our own Math anxieties.

        Teachers create unit plans to help them stay on track during the year. The unit covers a specific theme such as fractions; lesson plans are essential in limiting loss of instruction time, because the teacher is able to cover a specific theme each day. The lessons are differentiated to meet the needs of diverse learners including those with learning differences, gifted learners, and also students whose primary language is not English.

        Since all students learn differently, it is essential to provide children with opportunities that allow them to do Math in different ways.  This may also lead to class discussions that are beneficial to all students. Both guided activities allowing students to come upon their own understandings, and direct instruction are helpful.  Group work can also benefit some learners. It tends to be more helpful for stronger students. 

       Math practice should be encouraged for all students. The more a task is completed the greater the understanding.

References
Robert Ahdoot. “The Power of Yay Math.” TedXAIU. Online video 19 February 2013.
        Retrieved Web 11 September 2015.

 Small, M.(2013).Making math meaningful to canadian students, k-8.
        2nd ed. United States of America, Nelson Education Ltd.