The paths to "Eureka" moments: Teaching Mathematics in Secondary Education

Archive for April, 2012

x + students = culture of learning (Find x)

What are the building blocks to a classroom community and culture of learners?

One key foundational block in the structure of a culture of learners is to make the classroom a place where students trust the teacher and believe it’s a safe place to take risks. In doing this, the classroom becomes learner centered (core competency L1). By creating a safe place, a teacher can foster and encourage a student’s self esteem, their confidence in the subject matter, and their willingness to grow as a learner.

As a teacher, I will establish my classroom to be a safe place where respect and trust is mutual between my students and I. One of the ways I will do this is by getting to know my students individually. I will conduct a class survey at the beginning of the year to determine some of their interests. I will maintain regular individual conversations with them through quarterly letter writing. In addition, I will also share about my interests and likes/dislikes in math so as to relate to them at a more personal level. Finally, all questions will be valued in my class. There will be no such thing as a “bad question” so long as it is classroom appropriate.

The challenges of creating this safe culture for learning will be many. With so many students, it will take effort to get to know them all and ensure they know they are valued members of our classroom community. However, as long as a constant effort is being made to respect my students, I feel they will be able to help in creating a place where learning can take place.

Questions to consider: Is a book club actually a helpful strategy to use in a math class?  What kind of jobs could I create that are more than just “classroom chores” in my math class?

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It’s Art class, it’s a post office, no it’s Math class!

Pictures and letters in Math Class??

Two Writing-To-Learn techniques that I will be using in my classroom are illustrations/pictures and teacher correspondence. Encouraging my students to draw Illustrations and pictures as a routine part of our math assignments not only gives them a creative outlet but it provides students to see math in a different visual perspective. Corresponding regularly with my students in the form of short notes will provide feedback, produce cues for individualized instruction, give insight into the learning styles of my students, and finally, guide differentiation.

Both of these writing tools are learner centered.

Illustrations and pictures allow students to create their own visual aid to deepen their understanding of a concept. For example, if given a word problem, each of five students could read that problem and then draw out the important pieces they feel vital to solving the problem. Depending on the problem and the variables they chose to emphasize, multiple correct solutions could be found using the aid of different visuals.

Teacher correspondence through letter writing would be personal. Several times a year, I will ask the students to write a short letter to me which answer several prompts about the class material as well as how they are doing individually. As I respond to each, students will see their value and get immediate feedback on their misunderstandings. While this may be time consuming, I feel it will be worth it!

Discussion Question: Can we please talk more about Learning Logs, Notebooks, Sketchbooks, and Buttpads? Specifically Learning logs? With all this paper floating around, I’m seeing chaos if organization isn’t implemented right.

Creating a “Lightbulb” effect! How do smart readers think?

How can students engage in their reading?

How can students engage in their reading?

As a teacher, it is my job to teach reading strategies which enable students to think and become smart readers. One method I can use to accomplish this is through reading activities that emphasis techniques students can use before, during, and after reading.

For “before” reading, I like the KWL activity where students are asked to identify first what they Know about a particular subject, then what they Want to know, and then following the reading end with what they Learned. Through this activity, students will use their prior knowledge to spark interest and use scaffolding to build a new layer of knowledge. This activity relates to Standard T2: Intentionally Planned, as it is a planned exercise for students to complete before moving into new subject matter.

In terms of Mathematic State Standards, using a reading strategy like KWL addresses and enhances the category of Core Processes: Reasoning, Problem Solving, and communication. When my students are equipped with reading strategies they will be able to tackle tough word problems, work through new definitions, and dig deeper into class content.

Question to consider:

* Besides asking the students questions, what are some methods for inspiring an inquisitive mind? In other words, how can I encourage a lot of content for the “W” part of the exercise?

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Citation: Chapters 3-6 Subjects Matter: Every Teacher’s Guide to Content-Area Reading,

by Harvey Daniels and Steven Zemelman

What Kind of Reader am I?

At this point in my academic career, certain thinking mechanisms have now become simply automatic. Reading fits this category. However, as I read “Subjects Matter: Every Teacher’s Guide to Content Area-Reading” I found that this involuntary skill has been developed as a result of learned strategies. Several tools that I frequently use include: Visualization, Question, and Evaluation.

In the classroom, it will be my job as the teacher, to provide my students with a tool box of strategies from which they can use the most appropriate tools for their personal learning styles. To do this, I will first teach my students how to use the strategies effectively, and then post cues on my classroom walls to remind them the tools are always at their disposal. To implement the strategies in my lessons, I will assign pre-readings prior to class, and spend class time reviewing the text before jumping into math exercises and activities. My hope is that the students will in this way, be able to build on a foundation of learning in the classroom.

Discussion Questions:

1) What are some ways that these strategies can be introduced?

2) What is a good way to provide an incentive for reading prior to class?

Citation: Chapters 1-2 Subjects Matter: Every Teacher’s Guide to Content-Area Reading,

by Harvey Daniels and Steven Zemelman

(Prove/Disprove) Desk + Chair + Whiteboard = Learning Environment ?

Does classroom furniture make a difference?

The physical arrangement of the furniture in a classroom can be either a help or a hindrance to student learning. It is important that a teacher be aware of how students react to specific classroom arrangements so as to create the most effective learning environment within the given space.

As a teacher, “You are a placemaker, an individual who creates a place that supports teaching and learning to the greatest extent possible” (McEwan 2006). This can be done through the classroom set up. Specifically, rooms can be set up so as to be territorial or functional.

The classroom I am observing this quarter is designed in a flexible, yet territorial manner. Specifically, students are assigned specific seating in rows of rectangular tables. Sets of two tables are pushed together to form one 4-student desk. There are 4 rows of the 4-student desks with 3 sets of desks per row. The students face the white board and can easily move their chairs to work in groups. This structure keeps students focused and attentive to the task at hand, while allowing for the flexibility of different teaching strategies.

To one side of the room, there is a “quiet space”. This provides any student the opportunity to remove themselves from the noisiness of the class and work independently in a less distracting atmosphere. In this way, my mentor teacher has created a space that is conducive to multiple learning styles and removes unnecessary distractions.

By changing the seat assignments regularly, she gives her students the opportunity to work with multiple people in the class. This not only builds camaraderie amongst students, but allows students to learn from different people throughout the school year.

As observed in the classroom, furniture arrangement and structure are pivotal in creating an effective learning environment.