Building a Safe Place vs. Technology Grant
The PBL about building a safe place is for 7th and 8th grade students to come up with a solution to present to the Peoria community board. The students will come up with an idea for a community center that includes a budget, educational centers, fundraiser ideas and more. This PBL includes numbers and operation, algebra, geometry, measurement and more. I think this PBL activity involves several types of math and also connects with many other subjects as well. This PBL is a great example to me of what an effective problem based learning activity would look like. The PBL about the technology grant is about a teacher that wants to apply for a $50,000 grant for the low-income school he teaches at. He assigns his 7th and 8th grade students the task of coming up with a grant proposal to present to the board. The focus of the math in this problem is budgeting, I think this activity could have and should have incorporated more math concepts into the equation.
When comparing and contrasting this two different PBL's, each has things I like and dislike. Overall, I much prefer the set up of the "Building" PBL. I think it's much more organized, easier to read and more professional looking. I also think it incorporates more math into the activity, the mini lessons are easier to follow and more detailed as well. In "Technology", I do like that there are several questions for the teacher to use to prompt the students as well as specific examples for adaptations. The strengths of the first PBL in my opinion are the mini-lessons, the assessments, and the way the activity is written in general. The strengths of the second activity are the adaptions for special needs and gifted students as well as the prompts and role of the teacher. While I think math is the main focus of both PBL's, I once again do not think there are enough math concepts in the "technology" PBL. I like that there are different layers to the "building" PBL and therefore different types of math required.
Tuesday, January 31, 2012
PBL Review part 2
Problem Based Learning Faculty Institute
The website I found is from the University of California- Irvine, and it's a faculty institute about PBL. This website explains what PBL is and that it's a student-centered approach. It then goes into the criticisms and benefits of PBL and what the instructor's role is. The instructor is not to be passive but should model different problem-solving strategies and should ask the students higher-order thinking questions. The section on this website that I really like and thought was helpful is a chart of characteristics of PBL. There are 3 columns, WHAT, HOW, and WHY? An example is WHAT: Student-centered and experimental HOW: Select authentic assignments from the discipline, preferably those that would be relevant and meaningful to student interests. Students are also responsible for locating and evaluating various resources in the field. WHY: Relevance is one of the primary student motivators to be a more self-directed learner.
Other categories within the WHAT section are: inductive, build on/challenges prior learning, context-specific, problems are complex and ambiguous and require meta-cognitive thinking, creates cognitive conflict, and collaborative and interdependent.
The article is geared towards college professors using PBL strategies for college students. Although the context is a little more advance, the idea of PBL is the same. I did like the chart provided and thought it has good explanations of why and how to use PBL and why it works. Another reason I liked this website is that there are many examples provided with some student evaluations. I also liked that this website had some criticisms of PBL because I was interested in what they might be. As a future primary school teacher, I would try to find a different website when looking up information about PBL because this is not geared towards younger students. Although the ideas are the same, the language is more complex and the examples given do not apply to primary grade students.
http://www.pbl.uci.edu/whatispbl.html
The website I found is from the University of California- Irvine, and it's a faculty institute about PBL. This website explains what PBL is and that it's a student-centered approach. It then goes into the criticisms and benefits of PBL and what the instructor's role is. The instructor is not to be passive but should model different problem-solving strategies and should ask the students higher-order thinking questions. The section on this website that I really like and thought was helpful is a chart of characteristics of PBL. There are 3 columns, WHAT, HOW, and WHY? An example is WHAT: Student-centered and experimental HOW: Select authentic assignments from the discipline, preferably those that would be relevant and meaningful to student interests. Students are also responsible for locating and evaluating various resources in the field. WHY: Relevance is one of the primary student motivators to be a more self-directed learner.
Other categories within the WHAT section are: inductive, build on/challenges prior learning, context-specific, problems are complex and ambiguous and require meta-cognitive thinking, creates cognitive conflict, and collaborative and interdependent.
The article is geared towards college professors using PBL strategies for college students. Although the context is a little more advance, the idea of PBL is the same. I did like the chart provided and thought it has good explanations of why and how to use PBL and why it works. Another reason I liked this website is that there are many examples provided with some student evaluations. I also liked that this website had some criticisms of PBL because I was interested in what they might be. As a future primary school teacher, I would try to find a different website when looking up information about PBL because this is not geared towards younger students. Although the ideas are the same, the language is more complex and the examples given do not apply to primary grade students.
http://www.pbl.uci.edu/whatispbl.html
PBL Review part 1
Problem Based Learning, or PBL, is a learner centered approach to teaching. PBL can be used in any grade level classroom, as long as the material is developmentally appropriate. PBL gives students complex, real-world problems to solve that do not have one simplistic answer. The teachers role is to be the facilitator and ask questions, allow plenty of time, and provide resources for the students to use. The students role is to, in small groups, figure out what they know and what they need to know to solve the problem. The students then apply that knowledge to come up with a solution or multiple solutions to the problem. Problem based learning allows the students to use higher-order thinking, problem solving skills, reasoning, communication, and many other skills to solve problems.
Friday, January 27, 2012
Developing Mathematical Reasoning Through Games
The article I choose was written by Jo Clay Olson, a 25 year teacher from pre-k to high school. She wrote about her experiences with mathematical games and the relationship to mathematical reasoning. Engaging math games encourages students to explore number combinations, place value, patterns, and many other mathematical concepts. She put the three P's in place- Plan, Play, and Please be patient. With the three P's in place it provides a framework for teachers to explore mathematical ideas and discussion. When choosing a game for your students to play you must: play it yourself to gain familiarity, discuss ideas and how they can emerge in class, determine the level of competitiveness for you class, anticipate responses and outcomes, and create a list of questions to prompt students' thinking. When you Plan you must decide how you will introduce the game to your students, how you will decide teams/partners, what materials you need, etc. When you Play you should walk around the classroom after you introduce the game and listen to the conversation with the students, take notes on strategies used, and think of discussion starters. In Please be patient it is important to provide repeated opportunities for you students to play the game, and watch as the mathematical strategies change. In this article she provide three games to use, two for primary grades and one for intermediate. Include in these games are question prompts, and answers from her students, and "cautions" she found during her experience. Games are fun and create a context for students' mathematical reasoning. Games encourage students to respond different using different strategies and enhance further mathematical reasoning.
I enjoyed this article very much. I enjoy playing games and would love to incorporate games into my classroom. Not only does this article provide several games and tips to go along with them for math lessons, it provides reasoning from an experienced teacher. I liked the three P's strategies of planning games and can see myself using several strategies I have obtained from this article. I also liked that within the different game sections in the article, she provided question prompts and tips to further enhance students' thinking. I would like to use these game ideas and strategies in my math classroom.
I enjoyed this article very much. I enjoy playing games and would love to incorporate games into my classroom. Not only does this article provide several games and tips to go along with them for math lessons, it provides reasoning from an experienced teacher. I liked the three P's strategies of planning games and can see myself using several strategies I have obtained from this article. I also liked that within the different game sections in the article, she provided question prompts and tips to further enhance students' thinking. I would like to use these game ideas and strategies in my math classroom.
Olson, J. (2007). Developing mathematical reasoning through games. Teaching
Children Mathematics 13 (9), 464-471.
Reason abstractly and quantitatively
-Mathematically proficient students make sense of quantities and their relationship with problem situations
-Two abilities to solve problems involve quantitative relationships:
1. Decontextualize which is the ability to abstract a given situation and represent it symbolically and represent symbols as they have a life of their own
2. Contextualize which is the ability to pause in the process and think about the symbols involved
-Quantitative reasoning creates a representation of the problem, attends to the meaning of quantities, and knowing the appropriate properties of operations and objects
-Two abilities to solve problems involve quantitative relationships:
1. Decontextualize which is the ability to abstract a given situation and represent it symbolically and represent symbols as they have a life of their own
2. Contextualize which is the ability to pause in the process and think about the symbols involved
-Quantitative reasoning creates a representation of the problem, attends to the meaning of quantities, and knowing the appropriate properties of operations and objects
Tuesday, January 24, 2012
Video Analysis 1
The videos were about a fourth grade lesson plan on variables. The teacher, Mrs. Klein, introduced the concept of variables by assigning a number to each letter of the alphabet. The students were in groups and they were assigned various tasks to use the different variables to create words and assign numbers to the words. The tasks were designed to introduce variable and the concepts of the links between numbers and letters.
Questioning: Reflective task 1: Describe how the teachers questioning and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment.
The teacher uses prompts to get students to discuss and share their ideas throughout this lesson. By having the students explain and discuss with their peers and teachers it allows the students to bounce ideas off one another. Class discussion gets all of the students thinking and their creative juices flowing. This type of questioning and class discussion creates a positive classroom learning environment for the students to be successful.
Assess: Personal Reflection 1: What techniques do you use to determine whether students have learned the materials you are teaching?
Assessment is essential to determine whether students have truly learned the material you are teaching. Assessment can be informal or formal. Mrs. Klein used informal assessment for this particular lesson by listening to students conversations for understanding. She analyzed what the students could pick up on, what they were looking for, what they could see within the problems, and how they solved the problems. Another way to assess informally is through participation. Formal assessment is another technique to determine if the students have learned the material. Formal assessment could be a test, a worksheet, a project, etc. Through assessment, informal or formal, the teacher can determine whether students have learned the material.
Responding: Reflective task 1: Describe the student-teacher interactions during the task debriefing discussions and assess the effectiveness of these interactions.
During the debriefing of each task, Mrs. Klein asked the students to reflect on the work and share some examples with the class. Mrs. Klein prompted questions which allowed the students to share their ideas and theories about the tasks. Mrs. Klein gave positive feedback to the students and encouraged their theories and ideas. This type of discussion creates a positive learning environment and a positive student-teacher relationship. By having the students share their ideas and how they solved the problems, it allows for other students to learn from the discussion.
I enjoyed watching these videos, I think watching a teacher teach a lesson in an actual classroom setting is very beneficial. Not only is it beneficial to see how she teaches a math lesson, but how she conducts her class in general. There were several interesting classroom management strategies that she used throughout this lesson, clapping for example. Another reason I enjoyed watching these videos is to get ideas for my future classroom and how I will conduct my class. I liked the round group tables with supplies in the middle, that is not something you see often in classrooms and I liked the idea.
Questioning: Reflective task 1: Describe how the teachers questioning and the manner in which student responses are handled, contribute or do not contribute to a positive classroom learning environment.
The teacher uses prompts to get students to discuss and share their ideas throughout this lesson. By having the students explain and discuss with their peers and teachers it allows the students to bounce ideas off one another. Class discussion gets all of the students thinking and their creative juices flowing. This type of questioning and class discussion creates a positive classroom learning environment for the students to be successful.
Assess: Personal Reflection 1: What techniques do you use to determine whether students have learned the materials you are teaching?
Assessment is essential to determine whether students have truly learned the material you are teaching. Assessment can be informal or formal. Mrs. Klein used informal assessment for this particular lesson by listening to students conversations for understanding. She analyzed what the students could pick up on, what they were looking for, what they could see within the problems, and how they solved the problems. Another way to assess informally is through participation. Formal assessment is another technique to determine if the students have learned the material. Formal assessment could be a test, a worksheet, a project, etc. Through assessment, informal or formal, the teacher can determine whether students have learned the material.
Responding: Reflective task 1: Describe the student-teacher interactions during the task debriefing discussions and assess the effectiveness of these interactions.
During the debriefing of each task, Mrs. Klein asked the students to reflect on the work and share some examples with the class. Mrs. Klein prompted questions which allowed the students to share their ideas and theories about the tasks. Mrs. Klein gave positive feedback to the students and encouraged their theories and ideas. This type of discussion creates a positive learning environment and a positive student-teacher relationship. By having the students share their ideas and how they solved the problems, it allows for other students to learn from the discussion.
I enjoyed watching these videos, I think watching a teacher teach a lesson in an actual classroom setting is very beneficial. Not only is it beneficial to see how she teaches a math lesson, but how she conducts her class in general. There were several interesting classroom management strategies that she used throughout this lesson, clapping for example. Another reason I enjoyed watching these videos is to get ideas for my future classroom and how I will conduct my class. I liked the round group tables with supplies in the middle, that is not something you see often in classrooms and I liked the idea.
Friday, January 20, 2012
"Communication Speaks"
This article was written by a fourth grade teacher who changed the way she taught math to align with the NCTM communication standard. She began the change by simply starting to ask the students to explain their thinking- which began to make the class more interesting and engaging for both the students and the teacher. However, the students needed an opportunity to verbalize their answers and they needed prompts from the teacher. Some examples given of the types of questions asked were: Why is this so? Explain your thinking. Show me. How do you know? The next area of communication she worked on was listening, which is essential to communication. She started to stand back and allow the students to share with one another and determine different ways to solve problems. This forced the students to listen to each other, make connections, and think creatively. The next area of communication addressed was writing. She had her students create posters and their peers evaluated them. This demonstrated not only the importance of words but examples, the sequence of the way things are written, and the preciseness of vocabulary. After adding communication into the curriculum she asked herself , "So what are my students gaining from this added communication in math?" She could tell her students were gaining knowledge and benefiting from the discussion and sharing of thinking. As asking questions became a daily part of class, not only was the teacher asking questions but the students began to ask questions as well and wanted explanations. She saw her students take ownership and became invested in learning. As the article concluded, Robin stated that by asking one small question it can have a huge impact on teaching and learning. The students must be taught how to speak, listen, question, and write, this all takes time- time well spent according to Robin.
I enjoyed this article and thought it gave great ideas of how to incorporate communication into a math classroom. I liked that it was written by a teacher who has tried these methods and saw success with them. I would like to take these ideas into my own classroom because they are not only found to be effective but simple to incorporate. This strategies are beneficial in any subject, not only math. I think by adding communication to all subjects would be extremely beneficial to the students.
I know after reading this article and reflecting on my own math experiences, I do not remember using communication within the math classroom. I think it would have benefited me especially to answer and ask questions such as "why" and "how". I think by communicating in math, more students will like math and understand it better.
Kinman, R. L. (2010). Communication speaks. Teaching children mathematics 17 (1), 22-30.
I enjoyed this article and thought it gave great ideas of how to incorporate communication into a math classroom. I liked that it was written by a teacher who has tried these methods and saw success with them. I would like to take these ideas into my own classroom because they are not only found to be effective but simple to incorporate. This strategies are beneficial in any subject, not only math. I think by adding communication to all subjects would be extremely beneficial to the students.
I know after reading this article and reflecting on my own math experiences, I do not remember using communication within the math classroom. I think it would have benefited me especially to answer and ask questions such as "why" and "how". I think by communicating in math, more students will like math and understand it better.
Kinman, R. L. (2010). Communication speaks. Teaching children mathematics 17 (1), 22-30.
NCTM Process Standard: Communication
- Organize and consolidate mathematical thinking through communication: formulate a question, explain answers and reasoning, diagrams, mathematical symbols, writing to reflect on their work
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others: students need to test their ideas in the math community within the classroom, students will benefit from being a part of discussion
-Analyze and evaluate the mathematical thinking and strategies of others: students working on problems with other students
- Use the language of mathematics to express mathematical ideas precisely: gaining knowledge of mathematical language, students use of mathematical language, comparing mathematical expressions with technology tools
- Communicate their mathematical thinking coherently and clearly to peers, teachers, and others: students need to test their ideas in the math community within the classroom, students will benefit from being a part of discussion
-Analyze and evaluate the mathematical thinking and strategies of others: students working on problems with other students
- Use the language of mathematics to express mathematical ideas precisely: gaining knowledge of mathematical language, students use of mathematical language, comparing mathematical expressions with technology tools
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