Stage 6 Math Reflection

   

     Stage 6 Math Reflection: Math and Technology
      For my final math blog, I would like to share what really stood for me from Stage 6's  in class activities, online tasks, and lecture.  The obvious "Ah ha" moment is that math expresses itself everywhere.  This means that it should not be hard for us to connect math problems to daily applications and student life experiences to make it more meaningful.  It is hidden all around us (nature, pinecones, sea shells, counting, construction, baking, navigation, managing time, Darth Vader's mask, pineapples, sports, Mona Lisa, grocery stores,  calculating bank's interest rates, shapes, curves, patterns,etc). As a future educator, I can capitalize on this belief to increase students' motivation, interest, attention and emotion in math.  Something that I have learned from my math courses, is that mathematics is the universal language that we use everyday without realizing it.  I plan to use this strategy to help students discover and learn that math can be fun.

InvestingInOurYouth. (June 8, 2010). Investing in our youth - math is everywhere. Retrieved from https://i.ytimg.com/vi/Hh1M409ed1I/hqdefault.jpg

     Before this week's lecture, I had not heard of the SAMR model.  It is an acronym for Substitution, Augmentation, Modification and Redefinition and designed by Dr.Ruben Puentedura.  What a great reference to use because all technology is NOT created equal.  Computer technology is becoming more important in the classroom and it is our responsibility to consider how it might impact teaching and learning.  Overall, the model supports and allows educators to design, develop and inject digital learning that uses technology.  It is not only about using technology in the classroom, it is all about finding more meaningful uses of technology in teaching.  I am going to have to take more time to better understand this approach.  Obviously, I want to experiment with it and see how my lessons and assessments can be transformed considering the different stages of the model. The theory is that substitution and augmentation enhance student learning.  Modification and redefinition transform student learning.  At these two levels, technology allows for student analyzing, evaluating and creating.  In my opinion,  that is what we want to push our students thinking to include.
 

                  
Taken in class by Matt DiMartino, Thursday October 19, 2017.

     Another factor that resonated to me is that efforts to integrate technology into mathematical classrooms with games and apps can fail to make positive differences in student learning.  Students think games are fun and entertaining, but not all math games or apps lead to deeper understanding and greater competency.  Have a look at Dr. Boaler's video.  She highlights what a game should not do (emphasize speed) and presents three valuable math apps (Wuzzit Trouble, Motion Math, DragonBox) and a game (Mathbreakers)  that promote engagement with the math curriculum.  Other key features of superior apps and games are that they help students understand key ideas, see the math through animation and visuals and let the participants play and explore while learning mathematics.  Dr. Boaler's recommendations give your brain a workout by further developing brain muscles.  Now, I will have to consider this advice when choosing educational math games and apps for my students. 

     Creating digitally enhanced learning requires more than integration of new digital technologies. Dr. Boaler has presented criteria that will be useful when choosing the right technology.  It is important to consider and ensure that our chosen technology and practices actually enhance learning rather than limit it.
    Finally,  through blogging, I have documented some beneficial strategies, resources, and tips to help make math, a subject that students will love. There will be challenges presented by technology, but I will try and use them as a learning experience.   I look forward to implementing everything that I have learned in this course  in my fast approaching placement.


Thanks for any feedback and the support.

Stage 5 Math Reflection

     The modules continue to inspire me with informative strategies to make math meaningful to students in elementary school.  More importantly, I am learning how to develop knowledge and understanding of mathematics to practice and pass onto my students.  Key math principles were highlighted this week and include the importance of using intuition, drawing and representing, making sense of math, and understanding big ideas rather than memorizing.  My blog will mostly concentrate on these concepts because they left an impression on me, but I would like to comment on a webinar that I participated in.

Taken Wednesday October 11, 2017


     Since webinars are valuable educational tools, I look forward to incorporating them when needed. Bernadette and Jacob did a fabulous job of presenting their webinar about Universal Design and sharing ways to set up an encouraging mathematics classroom atmosphere by making changes to the environment's instruction, content, and product.  Overall, the webinar was very well -organized and included many interactive activities for this process; Answer Garden, input about how we could change ways to delivering instruction/questions, lesson content, and approaches to assess student learning.  The webinar was successful by providing us with ideas when considering the wide-ranging abilities of our students so that all are served and engaged.

Forsythe, G. (March 4, 2013). Universal design for learning.  Retrieved
     from https://www.flickr.com/photos/gforsythe/8527950743


     Dr. Boaler and other professionals continue to invite us to approach learning and teaching math with simple, important teaching practices; help students make sense of math by thinking of questions, and using intuition, encourage drawing and representation, and looking for the main ideas in math instead of memorizing all the little details such as formulas.   Have a look at how Sebastian Thrun, CEO of Udacity values intuition and math learning.

     This entrepreneur's message highlights understanding, thinking like a mathematician, and problem solving. These skills not only help with math but can be applied to citizenship and relationships. Thrun believes that intuition has the ability to empower and remove the fear associated with learning math.  I agree that the ability to use intuition can help students learn and embrace mathematics successfully. 

     Drawing and representing are other processes that can and should be developed to help students understand and solve math problems. Visualization allows students to remember and manipulate concepts. Focusing mathematical instruction on these approaches allows for greater flexibility when students display math ideas.

     The last important point that I learned this week is that practicing memorization can be problematic in math. While it is important to know certain math facts and hold them in memory, Dr. Boaler said that the best way for students to learn math is by deeply understanding the big ideas and not the little details.  She is not an advocate of practicing math facts over and over again or being tested on them.  I support the approach of organizing content around main ideas because I think that focusing learning around a few big ideas makes it easier for students to relate new knowledge to previously learned ideas.  After watching this video, I no longer believe that having a great memory is the key to excelling at math.  This was another one of my misconceptions of math.

                                    

Washington State University (2010). Big ideas. Retrieved from http://wsm.wsu.edu/s/index.php?id=789

     Of course, I want my students to feel good about math.  That means adopting strategies early on within my instruction that improves  student learning.  This week's module supplied me with many.


Talk to you next week.

Stage 4 Math Reflection

     Reflecting upon Stage 4's lecture slides, in-class and online activities, I determined that to make my math teaching effective, it is important for me to provide students with rich tasks to develop concepts and encourage flexibility with numbers.  I appreciated the handout of rich task criteria features; should be engaging and grounded in problem-solving, have a meaningful mathematical focus, provide opportunities for connections to life experiences and for the use of multiple forms of representation, allow for differentiation and support positive attitudes.  Looking at the all the attributes of rich tasks (Slide 3) makes me believe in this powerful quote by Pigott (2011). 

Retrieved from Slide 3 of Lecture 4, September 28, 2017

     It is so true that I have to put a lot of thought into my tasks and instruction so that I can make mathematics make sense to students and capture their interest.  Consider the first and second rich tasks within class; Which One Doesn't Belong (WODB)? and the Finger Counting Problem.

Retrieved from Which One Doesn't Belong, September 30, 2017

Photo taken by myself September 28, 2017

     I have seen both of these tasks introduced and practiced as a pre-activity in my placement and at an elementary school that I volunteered.  I like how the tasks have the potential to spark math talk, curiosity, critical thinking and mathematical "play" and allows for students to make connections among strategies and patterns.  This activity permits students to be engaged in math without realizing that they are doing math.  My favourite feature of (WODB) was that the questions are open-ended and all answers are right.  I think it encourages the freedom of expression (reasoning, conversation) that many students do not always experience in math.  There were plenty of opportunities for creativity in this task activity because it can be used when teaching geometry, shapes, 3D shapes, number sets, graphs and patterning.  I could do something similar with language and apply the task to any grade level in both subjects.  After initial responses, I would encourage students to work on their mathematical flexibility and find multiple responses.  More importantly, I would give students space and time to determine their different solutions and act on number flexibility.

     This brings me to my last point that I want to highlight, the value of mathematical flexibility, another strategy for success.  As a teacher, I must provide students with opportunities to build this flexibility.  After watching one of the videos, Dr. Boaler emphasized that those who are successful in math interact with numbers flexibly.  Upon further investigation, it was evident that it can help students solve problems and understand that there is more than one way to do this.  Flexibility helps with the comprehension of abstract math concepts.  How will I demonstrate and communicate to my learners about number flexibility?  It was suggested that one builds a culture of sharing and reflection in the classroom, encourage students to use different strategies and then analyze other students' problem solving methods.  Bringing attention to concrete, representational and abstract ways of problem solving work for me personally.  I am hoping that when I show my students a method, they can apply flexibility and show me what they know using more than my method. 

Boucher, D. (2015). Flexibility with place value. Retrieved from http://www.mathcoachscorner.com/wp-content/uploads/2015/12/Flexibility-with-PV-650x276.jpg


Hope everyone enjoys their flex week!
Until next time.

Stage 3 Math

     My main objective when teaching any subject area is to make it meaningful.  This week's in- class activities  concentrated on learning styles and creating a math board game, a perfect strategy to help students learn math in a fun and interactive way.  I understand that as a pre-service teacher, I must know the curriculum and my students.  Why is this so important?  It is because I want to reach all students and every student learns differently.  The VAK model is an acronym that refers to the styles of learning: Visual, Auditory and Kinesthetic.  After filling out the questionnaire, it is no surprise to me that I process information best through listening and speaking in scenarios such as a group discussion or lectures.  I am also a visual learner who prefers the use of graphics to access and understand new information.  I am definitely not a kinesthetic/hands-on learner nor would I be focused with this approach.  See my results below.

       I must understand the differences in my students' learning styles so that I can implement the best, creative practice strategies into their daily activities, curriculum and assessments.  When preparing lesson plans, there is much to consider.  It means thinking about differentiated instruction for learning materials (content), ways of learning (process) and ways of demonstrating learning (product).  I have to take the environment into consideration; how do my students work best? Alone or with others? Should the work setting be fixed or flexible?  Again, the goal is to foster a growth mindset in mathematics and this task is easier when I know my students' learning preferences.
      My partner, Giuliana and I created a Lego Measurement game that would work perfectly when teaching perimeter and area.  Game materials include;  Lego pieces, timers, dice, and grid paper.  Students can work with a partner or groups.  The objective is to roll the dice and whatever number is drawn, the participants must create a structure using the correct amount of Lego pieces to equal the area or perimeter.  More than one dice works great.  A timer can be introduced so that students are challenged to work faster and build the most structures.  Kids love games and Lego so we think that this would be received positively for students in Grades 4-6.  I see this activity as a way to allow students to solve math problems without realizing they are really doing math.  Games are fun, engaging and stimulating and often give students different perspectives.  I think that it is important for students to reflect about this experience and I would ask some strategic reflection questions as prompts such as; Can you connect the maths used today to something you already know?  What was fun when playing the game?  How can this game be changed the next time?

Thursday September 21/2017 Math Class

     

     While completing the on-line activities, it is evident to me just how closely related success and making mistakes are to each other.  I agree with Dr Starbird when he states that there is a problem in education when teachers discourage students from making mistakes.  His quote, "the result is that it encourages people to pretend to know more than they know." How true is this?  Success should not be the main focus in education?  I have to encourage my students to realize that success is built on failed attempts.  Mistakes and failure can be used to promote learning.  Professor Starbird's incorporates this strategy into his everyday structure when his students are encouraged to show their math work on a board so that others can watch and discuss the possibilities.  He feels that is is empowering and promotes creativity and I have to agree.  Michael Jordan is showcased in another video and he is one of my all time favourite basketball players.  Have a look here at his perspective.  

   

  I like the approach of highlighting the lives of athletes, dancers, actors, singers, role models etc., in the classroom so that students can witness the struggles, mistakes and perseverance that many have to overcome to  be successful.

Another informative week of strategies, games, learning preferences, mindset, how we can learn from mistakes, and math and speed.  See you next week!

Stage 2 Reflection

     There are many "Ah-ha" moments for me from Week two's class activities, readings, online modules, and comments made by classmates about conceptual learning.  I will not be able to share them all, but my blog will highlight the ideas that really stood out for me.

     While in class, we participated in a card game, Jeopardy, and a visual activity that emphasized that there are multiple approaches to answer math questions and watched a few videos.  The one video that really struck me was how Grade 8 students tried to solve a math problem that involved 125 sheep and 5 dogs. Have a look here. 

The participants needed to determine the shepherd's age.  Unfortunately, 24 responses did not make sense while only 8 students' answers did.  The message was that students who make sense of problems should be able to explain the meaning of a problem, plan a solution pathway rather than guessing or jumping into a solution attempt and continually ask themselves, "Does this make sense?"  Three easy steps and a great strategy that I plan to incorporate into my teaching when encouraging my students to use when solving problems.

     This is evident in the Mathematics document, Paying Attention to Mathematics Education which presents seven foundation principles for improvement in mathematics.  The document provides some great approaches and the first principle is to focus on mathematics.  On page four,  it states, "that all educators use a variety of critical thinking and problem-solving strategies to engage all students in making connections between content and process as they work toward a thought understanding of mathematics." There are six other foundation principles that can help all of us pre-service teachers when teaching math.

     I really enjoyed the math module that provided the characteristics of both Growth and Fixed Mindsets.  I think that this segment was very important because it described what mindsets are and how they affect the classroom.  We can revolutionize the way students think about success and intelligence in the classroom.  It takes an understanding that everyone can learn math.  Effort, hard work, and perseverance equals success.  It has nothing to do with looking smart or believing that people have a pre-determined amount of intelligence.  I have to admit that before this course, I felt that I had a growth mindset with some fixed mindset ideas.   I have learned that there is no room in math or any other subjects to have a fixed mindset.  I will continue to work on that and make a conscious effort to maintain a growth mindset for the sake of myself and students.  It will be our jobs to help our students embrace a growth mindset because it matters in schools.

    Another video that I watched about math messages highlighted that most students have fixed mindsets in math compared to any other subject.  As future educators, we have the knowledge to stop that.  Simply, it can be in our dialogue.  Telling students that they are smart can be detrimental.  Instead, we should tell them to not give up, work hard, and that failure can be a good thing.  Our responses and messages to students are very important.  We must constantly reflect and reassess the way we praise students' abilities and potential.

     Wrapping up, I see a definite theme to this week's activities, videos, and readings; tasks, advice, and strategies that teachers can use to encourage learning and a growth mindset in mathematics.  I am signing off until next week.
   
   
   
   

Math Week One Year 2

                                               MATHEMATICS WEEK/STAGE 1

 Well, it has begun.  Year 2 of Teacher Education and my first math blog of the new semester.  Actually, it was great week.  We started out with some math class activities that highlighted the importance of good dialogue with our students.   The professor started off by saying that she was going to show us a card trick that was easy and that we would understand it.  Everyone found the trick frustrating because we could not perfect it and many of us shut down.  The lesson learned here is that educators can foster mathematical understanding by avoiding words such as "easy" and developing a math talk learning community.

I liked how we created an answer garden about math.  It was interesting to see my peers' varied perspectives regarding math.  The answers ranged from awesome/engaging to annoying and complicated.  This is the reality and mindset of society and how we view mathematics.  This would be a great activity for our students so that we can have the conversation that all can learn math and get to the highest level.  It is up to us to use the right communication, resources and strategies that elevate students' interest in this subject.

I am excited to work with Rachel to construct a Webinar.  I have never presented one, but I am looking forward to our Web-based seminar.  Considering that we will be teaching the 21st century learner, this high tech educational tool is convenient and definitely encourages engagement.

Youngson, N. (July, 2015). Webinar [Online image] Retrieved from http://www.picserver.org/w/webinar.html

The online activities from the Math Mindset Module included videos highlighting math attitudes, myths, smashing stereotypes and information about brain growth.  Overall, these informative segments and research by a top notched professor at Stanford University and other experts showed us why and how we can improve motivation and interest in the elementary mathematics classroom.  I was able to relate my personal math experiences and perceptions (good and bad) to allow me to be more open minded about this particular subject.  I really enjoyed this video that you can watch here:

The message here is that there is no such thing as a "math person" nor is genetics a factor.  Everyone's brain is built for math and we all have the ability to understand math.  We just need to practice.  As teachers, we must make math a subject that students will love and embrace.  That is one of my goals.