Class Reflection- Angela McGreal June 23, 2009

I enjoyed creating this blog.  I have never created and used one before in this manner.  I think this will be a great resource for me when I beginning teaching.  This is a tool I can use with my students to communicate assignments, pose questions, respond to any issues they may have and communicate with each other.

Overall the assignments in this class were very helpful.  I gathered many new resources for teaching; lesson plans, instructional strategies and materials resources.  These will be invaluable when I start teaching.

For those of you who have middle grades math as a concentration, I want to share a book I came across that is available at the ASU library:  Math and Literature by Jennifer M. Bay-Williams and Sherri L. Martinie.  This book has many lessons/activities for students which revolve in some form around different story books.  An example of an activity in the book uses the story of Holes by Louis Sachar. Students calculate the volumes of the different size holes (cylinders) and compare the differences.  They further investigate the difference in dirt removal over time: one week, two weeks, and six months.

Angela McGreal Lesson 2: Barbie Bungee June 22, 2009

Angela McGreal Lesson 2: Barbie Bungee

Source:  NCTM Illuminations

Link:

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

Grade 8 NCSCOS Competency Goal 4: The learner will understand and use graphs and data analysis.  Objective 4.02: Approximate a line of best fit for a given scatterplot; explain the meaning of the line as it relates to the problem ad make predictions.

Lesson Overview

Students model a bungee jump using a Barbie doll and rubber bands.  They will collect data from the model bungee jump, construct a scatterplot and generate a line of best fit for this data and predict how many rubber bands are needed for Barbie to jump safely from a given distance. 

I like this activity because students will be engaged with the simulated bungee jump and they need to be reflective in their responses to questions posed.

I would use this lesson as is.  This is a good lesson that will actively engage students and doesn’t require much modification for the diverse learner as students will be working together and can support each other.  I particularly liked that a rubric is provided for assessing student work.

Angela McGreal Lesson 1: Discovering Pi June 22, 2009

Angela McGreal Lesson 1: Discovering Pi

Source: The Educator’s Reference Desk

Link:

• http://eduref.org/cgi-bin/printlessons.cgi/Virtual/Lessons/Mathematics/Geometry/GEO0001.html

Grade 6 NCSCOS Competency Goal 3: The learner will understand and use properties and relationships of geometric figures in the coordinate plane.  Objective 3.02: Identify the radius, diameter, chord, center, and circumference of a circle; determine the relationships among them.

Lesson Overview:

Working in groups of two, students will measure circumference, diameter and explain that by dividing the circumference of an object by its diameter you end up with pi.  This activity allows students to discover the formula for finding circumference using pi.

I like this activity because students are actively engaged through measuring and recording the circumference and diameter of several objects.  They reflect on their findings by describing their conclusions.

The lesson is well structured and I would use it as is.  Additionally, prior to a unit about circumference, I would read to students the story, Sir Cumference and the Dragon of Pi by Cindy Neuschwander; Wayne Geehan, which would provide background to the unit.

A Professional Development Initiative for Developing Approaches to Vocabulary Instruction with Secondary Mathematics, Art, Science and English Teachers June 22, 2009

“A Professional Development Initiative for Developing Approaches to Vocabulary Instruction with Secondary Mathematics, Art, Science and English Teachers” is an article which addresses the issue of incorporating vocabulary development throughout the various content areas.  Described in the article are various approaches developed and implemented during a yearlong research effort.  These approaches support students in building rich representations of word meanings as well as an understanding of word features such as roots, affixes and parts of speech.

 

Of particular interest to me was the use of vocabulary approaches in Mathematics.  Ms. Hash, the math teacher, engaged her students in constructing vocabulary learning by comparing and contrasting pairs of words through creating poems for two voices.  She also had students categorize words through the creation of visual displays of related terms with explanations of how the terms are related.  Through introducing words that shared the same root term as the mathematical term to be studied, the meaning of the mathematical term is reinforced through creating more connections.

The multigenre paper: Increasing interest, motivation, and functionality in research June 20, 2009

The article, “The multigenre paper: Increasing interest, motivation, and functionality in research” listed different approaches to the traditional research paper.  The author discusses and provides examples of one kind of research paper, the multigenre paper.  This particular type of research paper is unique in that students don’t just compile the research into one written work.  They write several pieces that integrate what they have learned from the research through different genres.  Students may create a birth certificate or a birth announcement to describe when and where someone was born.  They might create a newspaper article or a personal letter to talk about a traumatic or pertinent event in the person’s life.  Combining these writings of different genres may not flow together smoothly, but requires much thought on the part of the student. 

 There are several factors which make convincing arguments for the use of multigenre papers in lieu of the traditional kind of research paper.  The readability and research factors, the use of genres other than the typical research paper, the high level of effort required, the technical aspects of presentations, and the creativity involved indicate the positive aspects of multigenre papers. 

 This type of paper will support the diverse learner and enable the creativity of those who are not as academically inclined to shine through.

 Questions:

 1)     In mathematics, I can see using multigenre papers to research famous mathematicians.  Are there other applications for multigenre papers in mathematics?

 2)     Would a multigenre paper be a good alternative to a research paper if it is limited to 3-4 genres?

 3)     How would you modify a multigenre paper for an ELL student?

I poems: Invitations for students to deepen literary understanding June 20, 2009

The article,” “I” poems: Invitations for students to deepen literary understanding” points out that written reading responses can enhance student comprehension, as both reading and writing are viewed as constructive processes that require active engagement.  As students read, they begin to construct some understanding.  During writing they consolidate and enhance their understanding.  The result is better comprehension of the text.  Students remember ideas better when they have to transform those ideas from one form to another.  Student endeavors involve understanding and being understood.  Through the use of “I” poems, this can be accomplished.  In writing these types of poems, students use the first person point of view, becoming the narrator and expressing thoughts and feelings from this point of view.

 Questions:

 1)     How would an “I” poem be used in a mathematics class?

 2)     Can an “I” poem be assigned without a reading assignment?

 3)     Will students writing “I” poems feel restricted by thinking only in the first person?

Mathematics Instructional Strategy 4 June 15, 2009

Angela McGreal

Name of Strategy: Think-Pair-Share

Source (Where did this come from?):

• Pennsylvania Department of Education
• Instructional Strategies Online, Saskatoon Public Schools

Link to the Strategy:

• http://www.pde.state.pa.us/reading_writing/cwp/view.asp?a=196&q=98024
• http://olc.spsd.sk.ca/de/pd/instr/strats/think/index.html

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source:

Students are given a topic or open-ended question to think about, recording their thoughts on paper.  They then work in pairs to share their thoughts on the topic or to come up with a solution.  A combined statement is then shared with the class.

Explain what part of the standard course of study is addressed by this activity.

The Mathematics NCSCOS does not have a specific goal which this instructional strategy addresses.  However, this strategy reinforces and deepens any concept the student learns through thinking about the topic and discussion with his/her partner and the class.

Explain why you think this strategy will work. How does the strategy help your students learn?

Students are actively involved in thinking about concepts presented in the lesson.  When students have time to think-pair-share throughout a lesson, more of the critical information is retained.  When students talk over new ideas, they are forced to make sense of those new ideas in terms of their prior knowledge.

Mathematics Instructional Strategy 3 June 15, 2009

Angela McGreal

Name of Strategy: Journal/Reflection

Source (Where did this come from?):

• Instructional Strategies Online, Saskatoon Public Schools
• Pennsylvania Department of Education

Link to the Strategy:

• http://olc.spsd.sk.ca/de/pd/instr/strats/journal/index.html
• http://www.pde.state.pa.us/reading_writing/cwp/view.asp?a=196&q=98199

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source:

Students keep a journal to write about what they just learned; they should reflect about the mathematical concepts and how they might connect to other concepts or subject areas.  The teacher might set up a reflection page as a handout or a template for a journal entry.  A prompt or guiding question may also be used to steer student thinking.

Explain what part of the standard course of study is addressed by this activity.

The Mathematics NCSCOS does not have a specific goal which this instructional strategy addresses.  However, this strategy reinforces and deepens any concept the student learns through writing and reflecting.

Explain why you think this strategy will work. How does the strategy help your students learn?

Students who use journals are actively engaged in their own learning and have the opportunity to clarify and reflect upon their thinking.  Journal writing in Mathematics provides students opportunities to explain their thinking about mathematical ideas and then to re-examine their thoughts by reviewing their writing.  Writing will enhance student’s understanding of math as they learn to articulate their thought processes in solving math problems and learning math concepts.

Mathematics Instructional Strategy 2 June 15, 2009

Angela McGreal

Name of Strategy: Mathematics Circles: A Structured Approach to Problem Solving

Source (Where did this come from?):

Mathematics Teaching in the Middle School; vol.14, No. 4, November 2008

This is a journal published by the National Council of Teachers of Mathematics.

Link to the Strategy:

There is no direct link to the article.  It can be found in the Eric database and a copy of the article can be requested through ILLiad.

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source:

The author has struggled with ensuring that all students remain actively engaged in group problem solving activities.  As a result, she applied the same concepts found in literature circles to mathematics.  She developed a set of seven role sheets that would be helpful in problem-solving situations and began using them for a variety of applications.

As with the various roles sheets in literature circles, not all of the seven sheets need to be used simultaneously.  They are designed to be used flexibly, depending on the problem and the group situation.  The seven roles are:  Situation Summarizer, Vocabulary Master, Idea Guy or Idea Gal, Model Maker, Computation Kid, Connector or Link Master and Path Finder.

Implementation should begin with word problems that have few steps, so students can focus on their role sheets without being too overwhelmed with the problem solving exercise.   Students rotate roles as they solve problems involving similar mathematical content, so they can help one another in the varying roles.  Once they become familiar with the various roles students are ready to tackle more complex problems.

Explain what part of the standard course of study is addressed by this activity.

NCSCOS lists as a Major Concepts/Skills for each grade 6-8; Students will solve relevant and authentic problems using appropriate technology and apply these concepts as well as those developed in earlier years.

Problem solving is an objective for most of the NCSCOS Goals from grade 6-8.

Explain why you think this strategy will work. How does the strategy help your students learn?

Mathematics circles activities helps students with the process of solving complicated problems that may have multiple solutions paths or more than one solution.  Using the role sheets encourages students to hold their group members accountable for their work.  Problem solving can be valuable not only for developing new mathematical ideas, but also for deepening students’ understanding of previously learned concepts.

Mathematics Instructional Strategy 1 June 15, 2009

Angela McGreal

Name of Strategy: Pre-Reading- Review of Mathematics Text Format

Source (Where did this come from?):

CAROL… Literacy Strategies:  Reading Strategies for Mathematics

• http://www.ltl.appstate.edu/carol/unit3/unit3index4620_sum09.html

Link to the Strategy:

http://www.ltl.appstate.edu/carol/unit3/Reading%20Strategies%20Applied%20to%20Math%20Presentation.pdf

Give a thorough description of the strategy and how it will be implemented. This should be a summary of the strategy according to the original source:

An outline is created to show the structure of the text, which will help students understand how the text is organized.  This will aid in organizing student thinking and learning when reading the text.

Explain what part of the standard course of study is addressed by this activity.

This activity doesn’t address a particular standard; rather it addresses the overall need for students to “develop mastery of major concepts in specific grades”, as stated in the NCSCOS, The Mathematics Program, page 9.  In order to achieve this, students need to be able to comprehend the text.

Explain why you think this strategy will work. How does the strategy help your students learn?

When students understand the layout of the text, they are able to comprehend the information provided.  Knowing the structure of how the text is laid out enables students to quickly find information for review of the topic.