Friday, September 30, 2011

Warm-ups in Math Education

Based on my research and personal philosophy, the use of quick warm-up activities in class can be beneficial for several reasons. One of the most important reasons to use a warm up activity is for review for students who may not have not fully mastered the prerequisites. A warm up activity can be used to review prerequisites and to gauge student mastery.

As a warm up activity I’d begin my lessons by having my students complete several problems that cover prerequisites. Hopefully the warm up activity will also give me time to circulate among the students and have quiet one-on-one conversations. I’d use this discussion time to perform informal assessments on my students.

Saturday, September 24, 2011

Standards, Standards Everywhere

First of all I made the mistake of printing off all three standards so that I could do a side-by-side comparison. Even with printing out only my assigned standards, I still had over thirty pieces of paper to compare. This made things a little confusing! The first thing I noticed was that the NCTM standards had a “data analysis and probability “ standard, the Common Core (CC) had a “statistics and probability” standard and the CMP also had a “data analysis and probability “ standard. This meant that none of the CMP and NCTM standards directly aligned with the CC standards. The second thing I noticed was that the NCTM had standards that covered several grades (3-5, 6-8, and 9-12) while the CC had separate standards for each grade level 6th, 7th, and 8th and then a high school standard. Meanwhile the CMP listed the standards and then wrote the grade level beside the standard (6th, 7th, or 8th or a combination of the three). The way these standards were set up made it confusing ad near impossible to compare. In the end I did find similarities amongst the standards, but I could not find two standards from different organizations that completely matched up. As a new teacher, I'm not sure how I'd create a lesson plan that completely conforms to all three standards.

Appropriate Use of Technology - Barbie Bungee

For my lesson for Data Analysis and Probability for grades 6-8 following the NCTM standards I chose Barbie Bungee. I have to admit that I chose the lesson plan because my six-year-old daughter was reading the lesson titles along with me and she loves Barbies. Then I reviewed the lesson plan and found that it was a great way to teach data collection and prediction. In this lesson, students model a bungee jump using a Barbie® doll and rubber bands. The distance to which the doll will fall is directly proportional to the number of rubber bands, so this context is used to examine linear functions. Fun! It gets students' interest by asking, "Do you think the length of the cord and the size of the person matters when bungee jumping? Would it be smart to lie about your height or weight?" I think the kids would love it! In this lesson technology can be used to create a graph. To create a graph of the data, you could manually do it or you may wish to have students use the Illuminations Line of Best Fit activity, which is also included in the lesson plan. This lesson plan reinforces/teaches the meaning of the slope and y intercept within the context of this problem.


To design the lesson plan, the teacher used the following steps:
1) Learning Objectives
2) Materials
3) Instructional Plan
4) Questions for Students
5) Assessment Options
6) Extensions
7) Teacher Reflections
8) Standards

This lesson plan is great for the kinesthetic learner in that this includes hands on activities. This gets the students directly involved in data collection. It involves critical thinking in that students predict how many rubber bands are needed for Barbie to safely jump from a given distance. It gives the students a chance to use math to solve a real world problem. The students use problem solving to determine the number of rubber bands needed for Barbie to jump safely and to determine the minimum height from which Barbie should jump. If I were to change anything in this lesson plan, I’d use Ken instead of Barbie. ☺ I honestly thought that it was a very through lesson plan that included assessment of students and reflection questions. It even included extensions to the lesson plan. I couldn't think of anything additional to add.


http://illuminations.nctm.org/LessonDetail.aspx?id=L646

NCTM Standards and Expectations
Algebra 6-8
1. Use graphs to analyze the nature of changes in quantities in linear relationships.
2. Explore relationships between symbolic expressions and graphs of lines, paying particular attention to the meaning of intercept and slope.
Algebra 9-12
1. Use symbolic algebra to represent and explain mathematical relationships.
2. Approximate and interpret rates of change from graphical and numerical data.
Data Analysis & Probability 6-8
1. Select, create, and use appropriate graphical representations of data, including histograms, box plots, and scatterplots.
2. Make conjectures about possible relationships between two characteristics of a sample on the basis of scatterplots of the data and approximate lines of fit.

Saturday, September 17, 2011

Best Practices in Instruction

Best Practices in Instruction

Surprisingly, I found that I obtained totally different results when I performed a search for “best practices in teaching” vs. when I performed a search for “best practices in instruction”. I have to admit that the number of sites that came up when I performed my search overwhelmed me. It seemed that every institution, school district, and teacher had his or her own set of “best practices”. After reading through these best practices in instruction, I can say that my favorites were the following:

•Encourage student- faculty contact in and out of class.
•Encourage cooperation among students through collaborative assignments and in- class, group exercises.
•Encourage active learning by having students apply course content to real-world situations.
•Provide prompt feedback throughout the term.
•Emphasize time on task by indicating how long students should spend on an assignment.
•Communicate high expectations.
•Respect diverse talents and ways of learning by providing a variety of learning modes (written, oral, visual) that are culturally relevant.

In searching for the “best practices in education” I felt I was provided with too many general ideas whereas the “best practices in instruction” seemed to include specifics on how to achieve the best practices. “Provide prompt feedback throughout the term” is a practice I can start using immediately in the classroom where as “teaching for understanding” seems much more broad. In the end, I thought both searches were useful, but that I came away for many more useful ideas for the classroom when I searched under best practices in instruction. I loved Marzano’s instructional strategies that outlined specifics on everything from summarizing and note taking to homework and practice. This website gave me specific, useful techniques rather than just ideas of best practices. I bookmarked this page and will definitely use it again.


Sources:
http://www.ttms.org/best_practice/best_practice.htm

“Rethinking High School: Best Practice in Teaching, Learning, and Leadership.”

http://ritter.tea.state.tx.us/bestprac/bpc_instruction.html

http://www.ideapartnership.org/index.php?option=com_content&view=category&id=289&Itemid=141

http://www.tltguide.ccsd.k12.co.us/instructional_tools/Strategies/Strategies.html

Thursday, September 15, 2011

Comments on Best Practices in Education

I reviewed several “best practices in education” websites and the best practices I related to the most were the following:
1) Teaching for Understanding. I loved this as a best practice because it encompasses activities oriented toward higher-order thinking skills. Teaching for understanding requires a greater use of interdisciplinary curriculum and cooperative learning.
2) Use of Technology. I think it is a best practice to use technology. Technology is something all students will use in their future workplace and is an important skill
3) Educating All Students. I love this best practice because it emphasizes the fact that teachers need to change how they present material to reach all types of learners.
4) Integrated Services. I think this is an important “best practice” because it emphasizes team teaching and integrating services outside the school with the school system.