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Thinking Map: Mathematical Representation

  • Instruction is hands-on, with students using materials (or manipulatives) to experience math instead of memorizing facts
  • Students communicate through listening, speaking, reading, and writing about math
  • Activating students' prior knowledge prepares them to make logical connections, draw conclusions, and assimilate new ideas
  • As students are involved in hands-on activities, they construct their own tables, graphs, and charts. This helps them record and organize their thinking.
  • Webbing, and other engagement and exploration activities can help prepare students to comprehend reading assignments
  • Students are given opportunities to develop the art of questioning. Once they have learned how to ask relevant questions, they have learned how to learn.
  • Construct an anticipation guide - a set of teacher-generated questions that can serve as the students' pre/post inventory for a lesson

Fuentes, P. (1998). Reading Comprehension in Mathematics.

  • Semantic feature analysis - ask students to complete a chart that identifies the characteristics that concepts have in common

Important Concepts

Manipulatives in my classroom:

  • Non linguistic representations - students create a graphic that represents their personal association of a term
  • I normally try to employ manipulatives in the classroom - my kids get bored very quickly even when I use them

Barton, M.L., & Heidema, C. (2002). Teaching Reading in Mathematics and Science.

My Classroom

  • My host teacher LOVES white boreds (im not a fan). But I think they are good for quick computations. I don't like scanning the room at 20 white boards.

Drawing Connections & Conclusions:

  • I've used power points to lead games such as Math-O and Math Jeopardy. I've also done traditional lessons using PP - (kids did get bored with this)
  • We've also played games in the past using dominoes, dice, and cards.

Unit 2 Readings

READING in my classroom:

For this weeks Unit 2 readings, I chose key concepts that I found interesting and applicable to my style of teaching. I emphasized techniques that I've used in the past, as well as strategies that

will enhance learning in my classroom.

  • I like to stress the importance of reading the questions, and finding out what it is asking

Standards based curricula in my classroom:

  • In their warm up activities I like for them to write their definitions of words or terms
  • My host teacher uses a workbook that is standards based driven
  • The students have also contructed tables based on poles taken on the spot
  • In my lesson for this weeks Math Lab, we focused on statistics - mean, median, mode, and range. I rotated a series of real world problems using statistics that they may encounter. Students worked in groups - helping one another to understand the problems.
  • The articles this week focused on using manipulatives and other hands on activities to carry out the sequence and scope in Mathematics. The articles focused on understanding texts, and using a socio cultural perspective to facilitate learning. In addition, the unit emphasized the importance of utilizing constructivism in the classroom, while connecting content strands.
  • I like frontloading at the beginning of class - by having students do an old problem that connects to a new topic
  • When I do give word problems I try to include words, phrases, or places that they should be familiar with.

How I would like to improve...

  • I have been wanting to try the Semantic feature analysis
  • I would like for my students to conduct their own set of data and then find the MMMR
  • Manipulatives are Tools used to help students move from concrete beginner knowledge to an expert understanding of abstract ideas
  • It is assumed that students are using manipulatives individually or in small groups so that each student benefits through direct participation
  • I would like for my students to explore more using manipulatives and math discussions
  • Questions to ponder: Where should manipulatives go in the curriculum? As part of review to build understanding or connect ideas ? What discussion or activity will be conducted to assess that students have internalized instructions?

Reading Comprehension in my Classroom:

  • Place greater emphasis on statistics and data analysis
  • Students come from a naive perspective - their use of a manipulative may or may not lead them to the abstraction. Don't assume the expected mental associations follow.
  • Connect different content strands
  • Manipulatives can be used in a rote manner - and therefore require thoughtful consideration. They should be used as a means not an end to develop students' thinking.
  • I need to start writing on the board, my LO and my standard that we're doing for the day
  • Emphasize student involvement through group work, projects, and written and oral presentations
  • Stress the importance of proper treatment of all manipulatives and classroom materials
  • To emphasize the importance of math literacy, I've had my students construct word banks or word walls
  • Encourage students to use manipulatives when they feel it will assist their learning
  • Assess students using a variety of techniques: performance tasks, long term projects, oral presentations, and standard tests
  • Students should not be required to use manipulatives if they can develop other methods of achieving understanding
  • Evaluate academic outcomes with diverse student populations over time
  • In their game of jeopardy I've had categories that are devoted to interpreting texts

Concrete to Abstract With Tools, Manipulatives and Technology. pp. 69-111.

  • Take into account the unique needs and interests of students and help them connect math to their world by including lessons that utilize math in interesting contextual situations
  • The students have also done cutting and pasting activities, connecting phrases to equations

Standards-Based Curricula with Sample Lessons. pp. 112-150

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