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.

Creating Opportunities to Learn from Each Other

I recently watched Adora Svitak again on TEDTalk and I am reminded of how fascinating it is to hear kids explain their learning and understanding. I usually learn something new when I ask students to explain their thinking? As I start to teach more lessons, students continually amaze me with their creativity, intuition, and instinct. Adora is making the point that learning should be reciprocated in the classroom. Students are the leaders of tomorrow and it is important to provide opportunities for students to lead and succeed. High expectations is a big idea that has presented itself over and over in this program and I agree. I am thinking of ways to create more leadership opportunities in the classroom. I am also amazed at how much students love to help, show, and teach one another. When a student has a light bulb moment, there needs to be a way a student can share in their discovery and celebrate in their learning with others and/or at the same time acknowledging the classmate who taught them. Learning is reciprocated and appreciated in each way.

Technology and Math

What did I learn?
This week I re-learned about the Zone of Proximal Development by Vygotsky. I was reminded about the tension in learning and our goal as teachers is to reach the "zone" where students are not bored nor are they filled with too much anxiety where they feel they cannot succeed. I am also reminded about the engagement part of teaching and how we often have to be actors and actresses when we teach. 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. Good food for thought for Vaelentine's Day.

I also learned about about dynamic geometry in the computer lab. We went to the computer lab used Geometer's Sketchpad and Fathom. Sketchpad is quite fun and a very engaging way to understanding properties of quadrilaterals. Fathom was a great technology tool for students to not only graph but also understand the meaning. The big idea today was looking at how technology is shanging the way we think about math. Just a seed was planted today on how technology allows children to actually EXPERIENCE math. (Just like how video games can feel more life like, engaging, and now, get up out of your seat and actual dance to the music, this is where math is headed with technology.)

2. What do I have questions about?
I just wonder about the future and what it will look like with the iPods, smart phones, and all the new computer technology. I think it is exciting and great for teaching and learning. But, I also wonder about about the allocation of resources. Some kids will be exposed to the new technology and some will not. How will the new technology affect the achievement gap?

3. What are the implications for classroom practice?
Teachers wil need to keep up with technology and experiment with what's out there to find the best ways to use it in the classroom.

Measurement, Tangrams, and Multiple Entry Points

1. What did I learn?
I learned about activities involving measurement and also tangrams. Measurements do not have to be boring. "Flying frogs" with a cotton ball and paper clip is a way better lesson to discuss measurement, incorporate some physics, mean, and range. We also played with tangrams and did an activity called "The Giraffe." While I discovered being spatially intelligent may not be one of my strengths, I had a lot of fun trying to figure it out. Multiple entry points and showing kids there are lots of ways to be good at math was a big idea we discussed again. Maybe a child cannot understand abstract algebraic equations but they can do a tangram puzzle easily. Confidence and success in math is wonderful since math and emotions are often connected. Incorporating writing and creativity is another entry point for students to display their strength in math. My table group added how you could also make a poem, write a song or rap, or even a visual representation to make math concepts more interesting for students.

2. What do I have questions about?
How do you apply a tangram activity to real life and the students' lives?

3. What are the implications for classroom practice?
Math does not have to be straight out of a textbook and just involve worksheets. It could be fun and interactive. Multiple entry points should be a conscious effort when designing lesson plans. Teachers will need to stay current with technology to understand how blogs and/or voicethread can be incorporated in the classroom learning. This may take some risk but I think it is a risk worth taking.

iPod Touch Project: Differentiated Instruction (Update)

I chose to use the iPod Touch for student C, who has an IEP and gets pulled out for all subject areas: math, reading, and writing. It was hard to find the time to incorporate the iTouch since this student is in an out of the classroom a lot. However, I did have time during "Choice Time" to have this student use a letter recognition app. He was very engaged and learning too! I was also recently able to sit in during his parent teacher conference with the special education teacher there as well. The special education teacher said more practice with number recognition will help. I thought, iPod Touch would be a great way to get practice. I have been searching for a good app and excited to see how this works out and also assess if his number recognition has improved because of its use.

I think the iPod Touch is a great tool to have for this student. Since student C gets pulled out of class throughout the day, when he returns, he sometimes has to sit for a little while with nothing to do. For example, during math he comes in when there is about ten minutes left of whole class math time. This would be a great way for this student to have differentiated instruction. This idea just came to me, so my goal is to try this out this coming week.

In the beginning I wasn't sure how to go about using the Touches. But, the ideas are now starting to come especially for student C since he is not able to do the assignments the whole class is doing yet. The difficulty I am finding is finding a good app to fit exactly what I want. An app maker for teachers would be nice.

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I have also used the ITouch for science and literacy to record conversations with students. For science class, I recorded interview questions, and this was very useful to transcribe what was said and not have to write furiously to get everything down. In literacy class, I also used it to figure out fluency rate since the recordings are timed, and I was able to go back and listen to assess miscues and analyze student reading. Being able to record student voice as they read is wonderful and makes assessment a lot easier and more accurate.

If I am able to and have the time, it would be interesting to teach a lesson on expression using the ITouch. Each student would have a passage to read and the objective would be to read with expression. After recording all students readings, combining the recordings (I don't know how to do this but the idea sounds nice), a read aloud composed of student voices for one book could be done as the finished product. This certainly could be done with one student and one short book, and then shared with the class as a multimedia product with snap shots of the pictures/text in the book and the student's voice.