Professional Development

   Professional Development

       I would first like to say that the activity was so much fun! It really connected what we were learning during class yesterday and this concept will stick. Teacher professional development can oftentimes be boring. Depending on the timing of the professional development, teachers may think that it is a pain and they could be doing so many other things with their time. I have experienced this a few times over the last 2 years. When PD came around, I could see the look of annoyance on teacher’s faces and comments of “I could be planning or grading right now”. The purpose of attending these professional development sessions is to have the opportunity to make ourselves better. I embrace that opportunity to the fullest. I am always looking of ways to expand what I know about teaching and learning, professional development sessions help in that aspect.

       Over my 5 years of teaching, I have attended many different professional development sessions and the ones that stick out in my mind, were the ones that were fun and was something I could use in my classroom. I really enjoyed how “hands on” our activity was and this reminds me of a very fun PD I went to. The professional development I was able to attend was on Common Core Math and this PD came at a time when I was struggling to develop my own curriculum for my school. I was the only math teacher at the school, I was given the Common Core Standards and a good luck. I thought to myself “ I don't really know what these standards are so how can I make this fun?”. When I went into the PD I was pleasantly surprised by the hours we spent with our instructor. We did so many fun, hands on activities like learning to juggles and using manipulatives. It was wonderful and I was able to bring back so many things to my classroom.

       Another PD that reminded me of what we did yesterday was a technology one I went to in October. We learned the different ways to do a quick assessment in the classroom. We created our own games and played them as a group. Again, there were something that I could easily use in my own classroom. The instructor gave us easy to implement ideas and strategies rather than a lecture and a pamphlet.

       I wish professional development workshops were move vibrant and for the choices to be topics that are currently going on in the schools. It would be beneficial if more instructors did hands on, interactive activities with the teacher so we could use it as a tool in our classroom. Another idea for professional development is to give us teacher the opportunity to brainstorm with each other about ways we can bring what we just learned back into the classrooms. Isn’t that what these professional development days are meant for? For us to learn and implement things into our classrooms. I believe that if teachers had some time at the end of each PD to discuss ways to use what they learned in their OWN classroom, there would be less huffing and puffing about PD days and more excitement generated!

Algebraic Thinking

    Algebraic Thinking

           When I was young, I was (and still am) a lover of Algebra, so I want algebraic thinking to only involve letters, equations and solving for one answer. However this is not the case, as I have moved on in my math career and into teaching my thoughts on algebraic thinking have grown, matured and have changed. Algebraic thinking typically means for me looking for patterns and relationships. It allows for generalizations to be made about something, putting an equation or rule in place. I also think that algebraic thinking means taking some abstract concept and putting a face on it, or applying some type of rule. It is similar to other forms of mathematical reasoning because it challenges the student to think critically and provides a certain level of understand (some more than others). Algebraic thinking differs from other forms of mathematical reasoning like deductive reasoning. Deductive reasoning takes known facts and makes a conclusions.

         My students most use algebraic thinking when they see a concept for the first time. I usually start each unit out with some type of investigation. For example I gave my students many graphs of polynomial functions. I asked them to find some type of relationship or pattern between the number of zeros and the degree of the polynomial. This allowed for many conversations to take place, they had to develop some sort of rule to explain why a 4^th degree polynomial can’t have 5 roots, but a 5^th degree polynomial can have 4 roots. It took a little while for each group to sort through the graphs and come to some type of generalization. I think that this type of thinking paid off in the long run because I did not just give them the rule and memorize it, but figuring it out by themselves. 

        I imagine that algebraic reasoning can mean problem solving, justifying and proving. I am currently struggling with my students and their constant question of “why do I need this in real life?” In real life most of my students are not going to have to solve a quadratic equation by factoring or multiply rational expressions, but they will need to problem solve. The problem solving skills and thought process to answer the questions will help with real life problems. Being able to figure out what the “problem” states, what resources you have and what you need, setting up a way to solve the problem, actually doing it and then checking to see if you are right can translate into most careers.

          Math and the skills used in the math classroom (algebraic thinking and all methods of mathematical reasoning) all us to “sharpen” our critical thinking skills for us to use later on in life when we are given a problem that we do not know how to solve right away. We can use our algebraic thinking skills that were learned in a math classroom to overcome the problem.  Algebraic thinking also does not always have to be for the math classroom or on a homework problem. Anything that calls for problem solving or making generalizations will use algebraic thinking.