Reflection

             After reading through all my blog posts from the last quarter in addition to my own reflection over the last few months, I believe that I have gained a lot of useful ideas when working with children in mathematics.  I understand that as a class it would be impossible for us to cover the curriculum that is taught in the intermediate and middle school levels, therefore I appreciated the conversations that we have had in regards to dealing with teaching a diverse group of students.  What I have also come to internalize is that manipulatives MUST be used in the classroom.  Students need a concrete understanding of why a concept works, then students can move into the abstract; manipulatives offer students the concrete.

                This quarter I have also reflected on teaching by not merely telling students the answer or showing them short-cuts; real learning occurs when students are able to explain and make sense of their own ideas.  One of my favorite quotes from our readings this quarter stated; “my definition of a good teacher has changed from ‘one who explains things so well that students understand’ to ‘one whom gets students to explain things so well that they can be understood” (“Never Say Anything a Kid Can Say”).  I have interpreted this to mean that students need the opportunity to explore and discover the answers themselves allowing them to actively think and become engaged; therefore students are able to help each other and share their thinking.      

                The last big idea that I have reflected on this quarter is the use of technology in the classroom; technology can offer curriculum a fun and interactive way for students to learn. By engaging students into the world of  computers, students experience math virtually which then allows them the potential to enjoy exploring and playing with different concepts while they discover and make connections to their learning. 

              

               

Math Blog Feb. 28

In class tonight we were introduced to the online tool, Tinker Plots.  This tool allows students the ability to manipulate data on a graph and allows the user the ability to explore all the different attributes on a graph and how they can change when one variable is manipulated.  I love the idea of children making connections through their own exploration.  I know that as a student of math, I solve problems and understand equations at a pace different than many other people; in addition I enjoy learning on my own terms.  What I have learned from this is that by offering my students the tools that they need to explore a problem; chances are they are going to learn.  I have realized that math isn’t just standing in front the classroom telling students different concepts; it’s about group work, collaboration, exploration, and connecting to the real world.  I have also learned that teaching in this style is not easy and it takes a lot of planning and creative thinking on the teachers end, but I know as a student myself, this style of learning is much more fun and relatable to real life. 

The implications for this style of teaching in the classroom is huge.  Aside from student’s engagement through fun interactive means, I think that students will remember these concepts better.  One of my biggest struggles as a new teacher, is that I have never taught before, and aside from what I have been taught recently, my other frame of reference comes from my early schooling in math where there was a lot of plug and chug; as a result, I still struggle with the why question when students probe me for more.  Therefore, I have learned that it is important to educate students with the why explanation and through methods that allow students the ability to manipulate and explore new concepts introduced to them. 

Math Blog: Technology

1.  What did I learn?

Today was an exciting day!  We were introduced to some new technology that we could use in the classroom.  I love learning about the different ways to integrate technology into the class, I do not see it used a lot in my main placement, therefore the more I am exposed to it in other classes is great.   I am not afraid of technology, but if I am not familiar with how to apply it in the classroom, chances are that I will not, as a result even the minimal amount of exposure is helpful to me and my potential teaching strategies. 

For example, in my dyad placement I visited a neighboring 6^th grade math class several times; this particular math teacher loves technology and using it with his kids.  On one of my observations of his class, he told me about using the graphing calculators with temperature probes to go outside to take data sample of different things.  I did not get a chance to ask him specifically how it worked, but I got a better understanding after class on Monday.  If each student had his/her own graphing calculator along with a temperature probe, once the data is collected the calculators are connected into a computer and can be graphed comparing all students’ data! Amazing and so cool! 

2.  What do I still have questions about?

What are some good teaching resources for learning about different ways technology can be used in the classroom?

3.  What are the implications for classroom practice?

The implication for the use of technology in the classroom is huge!  Kids today are not strangers to technology, I am sure many of them could run circles around me in some areas.  So as a result, using technology with students will get them engaged and will allow them to use a tool that they are already familiar with to facilitate their learning in new areas.  I think that a lot of fear still exists regarding technology and how to “control” it, but if we allow our students the opportunity as well as the trust along with proper expectations, we can allow our students the ability to access so much more knowledge than one person can facilitate. 

Math: Feb. 7

1. What did I learn?

I enjoy our math class a lot; I never leave feeling overwhelmed…well maybe a little overwhelmed at the idea of the abundance of curriculum we will have to learn, but our professor does a great job telling us like it is.  I really appreciate her honestly as well as her ability to support us as new incoming teacher.  Our professor does a great job informing us about the areas where she believes teachers need to do a better job at teaching, in addition to the importance of making our lessons inquiry based.  I believe that as a new teacher I will be faced with many challenges, challenges that I never even prepared for, but if I can begin my career with the intentions of making math fun for my students, then I believe that I may make my life as a new teacher more manageable.    

2.  What do I still have questions about?

I wonder what a lesson of math would look like in your class.  How would you include a lesson about new material and at what point in the lesson would you facilitate this knowledge? And would the students all work on the assignments together? Would the assignments be turned in at the end of class?

3.  What are the implications for classroom practice?

I think that as a new teacher unafraid of technology, I will be able to challenge myself to find more interactive ways that my students can about mathematics.  I enjoy the idea of having the freedom to take what has already been created and modifying it for my purpose as well as my student’s needs.  I think that there are so many resources out in the world of education and through collaboration as well as workshops we can find more effective ways to teach our kids math.    

Math Blog 4

1.  What did I learn?

Class today began with an overview of creating a lesson plan. From this discussion I picked up some key ideas that I appreciated.  The first was that when planning a lesson always make sure that the objective is measurable; if the objective is not measurable it can be extremely hard to know whether or not the students have learned anything.  The second idea was that through planning a unit in mathematics it is helpful to follow these tips; take problems out of the text book that are not required as homework and use them on a test, create your final test first and work backwards based on what you want your students to know, and make sure to always do the homework problems that your students do.  I also enjoyed the ideas shared from the book called “What’s Math Got to DO With It.”  One of the ideas from this book states that students are motivated by their intrinsic success, or in other words when they feel successful. Therefore, as a math teacher it is incredibly important that I set up my students for success and help facilitate their own learning while doing my best to explain the same problems in multiple ways because no learner will be the same. 

2.  What do I still have questions about?

After class, I was left feeling overwhelmed at the task at hand.  I have many questions regarding how I will ever learn teacher strategies to all the concepts that my students need to know.  Fortunately I am learning that I will not know everything right away and my learning as a teacher will be a climb, therefore my goal will be to not become discouraged and frustrated at the challenge and instead take every challenge as a learning opportunity to improve myself as a teacher.

3.  What are the implications for classroom practice?

The implications these ideas will have on me as a teacher will be huge.  I understand that as a new teacher I am going to be at a disadvantage over any teacher who has taught before based solely on fact that I lack experience, but I have to remember to put it into perspective and to think back upon how far I have become since last spring and the leaps and bounds I have made since then.  I have accepted that I will be a life longer learner as well as a lifelong student and I believe in myself.   

Math Blog 3

1.  What did I learn?

In class today, our groups finished our GapMinder data tables and placed them on display for the class to see.  GapMinder is a virtual program that contains data on various things from around the world.   As a group, we each choose data to represent a story and then worked to compile a visual that would represent that story.  The purpose of this assignment was made very clear at the end of class when we debriefed about what we gained from this activity.  The end result was as follows: people construct data differently and people present information differently.  The lesson learned is that as a teacher it is very important to clearly present; just because it makes sense to you does not mean that it makes sense to everyone else.   

2.  What do I still have questions about?

When group members have completely different outlooks for presenting something visual, how do you help to facilitate the situation so that both views are included? Or can they?

3.  What are the implications for classroom practice?

The implication for the classroom is that required knowledge can be learned and taught in fun, interactive ways.  As a class we were given the lesson of producing a story through a data table; what the story was was left to our own interests.  This gave us, the students the ability to take our own interests and incorporate it into what the teacher wanted us to know.  Giving the student choice in their learning can be a very powerful tool. 

Week 2 Blog

1.  What did I learn?

I was able to take a lot of useful ideas from the assigned reading for class; the reading was titled “Never Say Anything a Kid Can Say.” This is an article written by a practicing teacher regarding what she has learned, and seen to work, when teaching children.  The main idea realized by this teacher was that by merely telling students the answer or showing them short-cuts, students don’t learn; therefore she believes that real learning occurs when students are able explain and make sense of their own ideas.  One quote that I really liked from this articles states, “my definition of a good teacher has changed from ‘one who explains things so well that students understand’ to ‘one who gets students to explain things so well that they can be understood.”  I have interpreted this to mean that students need the opportunity to explore and discover the answers themselves allowing them to actively think and become engaged; students are able to help each other and share their thinking to one another.    

2.  What do I still have questions about?

When students are exposed to new ideas or concept, shouldn’t the teacher model different strategies in the beginning to help them get started?

3.  What are the implications for classroom practice?

The largest implication this methodology would have on the classroom would be that the focus would be taken from the teacher and placed onto the students.  The teacher would help facilitate their learning by asking them the best possible questions and encourage students to listen to fellow classmates for strategies.

Week One

1.  What did I learn?

In class today we worked in partners to solve algebraic math problems.  After the first problem, counting the garden squares, my partner quickly solved the problem and immediately shared her solution with me.  I found it great to hear how she solved the problem, but I had needed more time to solve the problem for myself; in addition the method she developed differed from where my mind was trying to go.   I immediately noticed that when I did not have enough time to solve the problem myself, listening to how other people solved the same problem did not help me; it confused me more!  For the second problem, my partner gave me more time to solve the problem before we shared our thinking; from there I was able to understand her method.  I found my situation interesting because I could imagine the same scenario occurring with elementary students.  From this I learned that students need individual time to process, and the amount of time to process will vary for each student. 

2.  What do I still have questions about?

Is it ok to allow students the option to work independently or with a partner? What if a student prefers to always work alone?

3.  What are the implications for classroom practice?

The implication for classroom practice is that students learn differently and students think through problems differently, therefore it is important that a classroom cater to all the needs of the individual learner by offering a variety of opportunities for each type of learner to thrive.