What did I learn in math class this winter quarter?

I learned a ton about math this winter quarter! Here is a list of big ideas that stuck out to me:

• It is important for students to explore and experience math. This involves moving from concrete to abstract.  Manipulatives can be a great tool to for students to experience and understand concrete understandings first.  A deeper understanding and connections overall in concepts and formulas can be better grasped this way.    

• Manipulatives we used in class that I had not used before included: probes and a graphing calculator (I have to find my graphing calculator - good to know it's not obsolete), beans, algebra tiles, flying frogs (cotton ball and paper clip), poker chips, a square piece of paper, and tangrams.  I also learned about virtual manipulatives and http://www.nctm.org is a good resource for that.  I also saw how a website like gapminder.org  can allow students to see math as a part of their history and lives.  Understanding graphs stood out with using gapminder and a gallery walk interpreting other group's graphs. 

• Technology is changing the way we think about math.  Teachers need to keep current and experiment themselves with how to integrate society trends into the classroom.  With website like http://www.wolframalpha.com/, this changes the approach to teaching math.  Students being able to verbally explain their thinking will be more a part of the assessment of student understanding.

• There are different ways to be good at math.  It is important to have multiple entry points for students to be able to experience success in math.  Creative writing, using tangrams, and logical thinking are some different areas.  Math has a strong emotional connection and it is important to know your students and try to decrease the math status is a classroom.

• I learned it is not only important for math teachers to explain math well but it possibly more important for the students to “explain things so well that they can be understood” if students were truly going to learn mathematics. This reminds me of what was said in class about how kids will learn more from each other than they will from you- the teacher. Asking good question that produce thoughtful thinking and fruitful answers is skill needed for teachers.  A teacher's role now is more of a facilitator.

• Group work!  Creating a culture of productive group work in math was added to my teacher tools.  Participation is not optional.  I learned the strategy of having group members responsible for each other's learning.  I like this idea of teamwork.

Lastly, in addition to learning about math this quarter, this class was great because of the discussions we had about the human relations aspect of teaching as well.  "At the heart of teaching is care."  Showing kids you care and teaching kids to care for one another will make the world better in the future.  (I shared this theme with my first graders and even they looked at me with a funny first grade glare, I know they felt the encouragement).  I like the reminder about the engagement part of teaching and how teachers often have to be actors and actresses when we teach.  I am appreciative of the experiences shared about the realities of being a new teacher, diversity and judgement, and the humor and frankness that was also incorporated to our math class.    

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Scratching the Surface with iPod Touch Project

My views using the iPod Touch to support differentiated instruction is still the same from my last update. I used the Touch for Student C mainly because he is not able to do the same work the whole class is doing. I have continued using the Touch for math with student C because when he comes back to class, there is still ten to fifteen minutes left during math and the rest of class is usually doing independent work. With the Touch, Student C seems to be always engaged using either a numbers recognition app or simple arithmetic. I came to find out, he uses one at home too.

Finding the time to incorporate and experiment with the Touch was the hard part. After reading some of my comments from my last update- yes, I think using the Touch for transitions would be a great idea. With my class the only concern I have are the students who I foresee rushing through certain assignments just to use the Touch. This has been the case for some students when using their Netbooks. They rush through writing or math so they can go onto Dreambox or Coolmath.com. Even with their own personal laptop to use, the students are now preferring to use the large computers. There was an interesting discussion in class about the small size of the Touch and perhaps an iPad maybe would be of better tool to use for instruction.

For one of the my classes earned parties, the class chose to have an electronic games party. Students brought in their little Nintendo DSi and their parent iTouches. For students that could not bring any, they were able to use their Netbooks. There were about four iTouches that the students brought from home. This made me think about another discussion in class about how technology is a big and growing part of our society, and with this being part of culture, how then are we going to integrate learning with technology? Let me tell you, every single one of the students were on task that day! It was also interesting to be able to read an email from one of the parents in concern with the electronic handhelds. This parent did not like the idea of students bringing in high end toys in a public school because she thought it promoted materialism and student's that did not have these types of games would feel left out. This added another food for thought with the use of technology- getting parents on board.

Personally, I am all for the use of technology and integrating it into the curriculum. I like the way the iTouch adds another entry point to learning. I think I was only able to scratch the surface with my ideas on how to incorporate the iTouch for different students. Someone should write a textbook about this. It is also a great teacher tool to record student interviews, record how students read and assess their fluency rate, and record a lesson given. All of these can be used to better assess students, share with parents, and also help a teacher assess themselves.

Emotions in Math and www.wolframalpha.com

1. What did I learn?
From the article reading this week, I learned again how children and adults have strong emotions when it comes to math. It is interesting to see that just because a child is good at math still does not necessarily mean that he/she likes math. It is also encouraging to read that a student who may not be good at math but continues with it, still could end up in a career using math all the time. It is important as teachers to know your students and try to find an area in math where a child can succeed to build confidence. It was also interesting in the article, to see where other children perceive their peers to be good at math and compare that with the reality of their internal perception.

Another interesting discussion we had in class involved remembering that "children have a right to fail," and we also talked about how teaching is also about human relationships.

I also learned about www.wolframalpha.com. Wow! And what an impact this type of website has for teaching. It changes the idea of handing out worksheets for homework.

2. What do I have questions about?
I'm wondering how to incorporate homework and assignments when there are websites, like wolframalpha.com out there for students to get answers and also the "show your work" part can be found.

3. What are the implications for classroom practice?
Again, technology and the web is impacting classroom learning. Now, teachers can say "watch this or research how to solve this" and then lets discuss what we found. Explain your thoughts and thinking will become more involved in assessment if answers to math problems can be easily found on the web.