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