Teaching Children Mathematics - Polygon Properties

Summary:

This article focuses on teaching elementary students, grades three through five, the properties of various polygons. The article starts by introducing the activity and explains why it is appropriate for the grade level at hand. It also goes into explain the standards and how the activity is associated to them. The activity gives students a group of many different polygons, both regular and irregular, with various numbers of sides. Students are to sort the shapes by number of sides or other contributing factor. The article explains how the activity can be adapted for other age levels and goes into detail explaining why it is important to teach properties of polygons at this age. Students were able to apply this activity to real life situations, for example, eating crackers that are quadrilaterals.

Application:

Overall, this is a good activity for students and it can be very beneficial when learning shapes and classifying objects. I would use this activity on students of a similar age because it seems appropriate, especially with the explanation of the standards involved. I think this activity is great but can be pretty short in a classroom. This can be used for measurement skills as well as, students can measure length of sides and angles of regular and irregular polygons. The article left out ways to apply this activity to other parts of math and overall seemed slightly repetitive. I feel that this activity should be a small activity of many put together, I would have liked to hear about more examples.

Rodrigue, P, & Robichaux, R. (2010). Polygon properties: what is possible?. Teaching Children Mathematics, 16(9), Retrieved from http://nctm.org/eresources/view_media.asp?article_id=9290

Manipulatives Blog

1. How do you hold all children accountable when using manipulatives for an activity?

When working with manipulatives during class time, teaches need to be aware of students actions and behaviors. Teachers should be doing constant visual checks on students to make sure they are staying on task and completing necessary requirements. A good way of keeping students on task and putting them with a partner, especially one who isn't a buddy they could get in trouble with. This will keep students focused on the problem at hand rather than playing around with something else. Teachers can also give students a chart to document their progress/data with the manipulatives. They can also ask students what they have learned whether it be in a journal or vocally to the class. Lastly, teachers can give students checklists to make sure they stay on tasks with the requirements of the manipulatives.

2. Why do people say not "hands on" but "hands on minds on?"

Manipulatives should involve much more than just being hands on. They need to connect with the student so they can take the knowledge from the manipulative and apply it to something else. This is where minds on comes into play. Students should be cognitively engaged with the manipulative, learning and discovering new things. If an activity is just hands on, students can simply be "playing" and not focused on learning how to do the tasks in front of them. No matter how hands on a manipulative is, it needs to apply to the students learning.

3. How do the process standards fit in with the manipulative activities?

After discovering more about specific manipulatives today, I was able to apply them to the process standards with more understanding. The manipulatives can expand students communication through working in groups and talking with other students about the manipulatives at hand. Problem solving is expressed through students discovery of manipulatives and their ways of working through them. Students use their skills of applying prior knowledge to learn how to solve problems when using manipulatives. When students are left to guess and check using manipulatives, they are using reasoning and proof. This can be done using blocks and discovering their attributes. Some manipulatives cover more than one content area when used. This connects many disciplines and helps students connect all mathematics as a whole rather than specific sections of mathematics. Lastly, students will use representation when working with manipulatives as they organize and record information to solve problems. Representing students work is shown through filling out charts or understanding the relationship between mathematical problems.

Technology Reflection

After participating in math methods for almost a semester now, I have much more knowledge on how to incorporate technology in the classroom. This class emphasizes the use of technology more than any other class I have taken by far. The Smart board is a creative and impressive piece of technology to use in the mathematics classroom. It can be used to do many different mathematical equations and procedures. I had no clue how to use one walking into this semester but, now I feel much for confident using it and feel that I could definitely incorporate it into my own classroom.

After using the math applets in class I found math a lot more exciting and actually fun. Math became more of a game rather than a chore. Also, we created wikis as well. I liked the wikis because it kept us organized and took my writing to a different level. Mathematics as a whole has completely changed and improved with the use of technology.

The Geometers Sketchpad is another handy tool for technology use in the classroom. I liked being able to learn geometry and discover new things about it by using the software. It never got boring and I enjoyed using it and wanted to learn. This is incredibly important in a classroom because students can pay better attention and learn geometry in a much more hands on and creative way. With these and many other technologies like Inspiration and the video camera software, I was able to learn just how important technology in the classroom really is. I also learned that it is becoming more and more dominate and should be adapted into lessons as much as possible.

Error Reflection

Looking at and understanding the errors in Math Methods definitely gave me a better insight on the many mistakes students can make. I realized that students will encounter all types of difficulties in mathematics at all different age spans. Also, students can make errors for many reasons other than the assumed problems of rushing or simply not paying attention. Many students combine rules from other problems or change rules to fit their needs. In a student's mind, these changes make sense because he/she feels like they are getting the right answer.

Teachers need to be aware of the varying needs of each and every student. No student is alike and there will be all kinds of mistakes made. Teachers need to never assume that a student is not trying but always help a student to see if they are making a simple error in work that can be easily corrected. In general, I feel a lot more comfortable with understanding the many problems that can go into a mathematics equation and ways to make students learn easier. I feel that all the hands on activities we did gave me tons of ideas to use in my own class. I especially liked the method Dr. Grant taught us on division. It simplifies the problem and makes everything easier to understand. I will feel comfortable implementing these learning tools in my own classroom.

Mathematics Teaching in the Middle School - Tech-knowledgy and Diverse Learners

Tech-knowledgy and Diverse Learners

This article explains the need for more technology in the classroom and the correct ways to use technology to the fullest. It went into detail about the effects on technology on students with special needs and English Language Learners. When using technology on students, it creates a great way of covering all areas that need to be addressed. Students get a visual and can create things without having to have it physically in front of them. This will really benefit students who tend to get system overload for multiple pieces of work to do. Also, technology in mathematics can be used as a self check when completing problems so students do not have to have as much confusion in the long run. There are numerous programs out there that are advanced enough to greatly benefit an entire classroom of students will all sorts of personalities and backgrounds. The article gave many examples of what to use and when to use it along with visuals.

This article shows math in a new light and really focuses on the future of mathematics. One thing I did not like about the article was that it discussed the problems with ELL students but never went into detail or gave examples of the technology that can help the students like they did for students with disabilities. I feel that this article opened my eyes to a lot of the things schools should be using now rather than worksheets and great ways to implement them into the classroom. I feel though that this article forgets that with all of the budget cuts, some of these opportunities and programs might not be available at every school. In general, I learned the importance of technology on all students no matter what their level in school is.

Suh, J. (2010). Tech-knowledgy and diverse learners. Mathematics Teaching in the Middle School, 15(8), Retrieved from http://my.nctm.org/eresources/view_media.asp?article_id=9197

Teaching Children Mathematics - Teaching with Cognates

Teaching with Cognates

This article focuses on the challenges students and teachers face when trying to facilitate for English Language Learners. It goes into detail about the strict guidelines that are implemented into the school which leaves teachers struggling to find ways to help students be more familiar with the English Language. Many teachers are now relying on cognates, words in two languages that share similar spelling, pronunciation and meaning. These cognates benefit students and tend to help seal the gap between the two languages and help students communicate more effectively. There are many cognates associated with mathematics teaching that can be used to help students progress in mathematics. Teachers can use word walls to help explain the relationship between the two words in the different languages so students have a better grasp on the similarities.

I really liked this article because it made me think about a topic that I am very unfamiliar with. I never really process the likelihood of having a student in my classroom with a different dominate language than everyone else in the classroom. I can only imagine the confusion of all parties involved, especially the child himself. Using cognates seems like it could be a huge break through fro students trying to master English. They could even be put into a card game like memory where students have to match the Spanish word to the English word or used on flash cards. The opportunities are endless but need to be instructed in order for students to achieve at their highest ability.

Gomez, C. (2010). Teaching with cognates. Teaching Children Mathematics, 16(8), Retrieved from http://www.nctm.org/eresources/view_media.asp?article_id=9233

Assessment Article - Journals and Portfolios: Alternative Assessment for Preservice Teachers

Summary

This article expresses the importance of alternative assessment and benefits. The author emphasizes how she uses journals in her own classroom. Journals can be used as open-ended responses or as prompts. Open-ended responses are rewarding because they can have a varity of answers. Students can explain what they have learned, pose more questions, or even look to the future. This is great because students can feel comfortable about their grade without having to fear a test or quiz. Journal prompts can occur anytime or day. They are when the teacher gives students a topic or question about students write on that specifically. This type of journal can show where students are in their learning compared to others and what they understand.

Application

Journals can be beneficial in any classroom and are easy to do. Some pros are that they can be fun and help students not only reflect on their mathematics class but also work on writing skills. These journals will also be great to have to look back on in the future. I feel that some cons may be that students are not going to be assessed over everything they know; just a broad overview. This could leave some students to fall behind in mathematics. In general I think they have a great purpose and help students be more confident with assessment instead of dreading a test.

Liebars, C. S. (1999). Journals and Portfolios: Alternative Assessment for Preservice Teachers. Teaching Children Mathematics , 164-170.