During this unit there will be an in-depth explanation of the problem solving strategies discussed in Unit 1. At the end of this unit you will be asked to write a formal lesson plan that implements at least one of the strategies described below in the correct manner. Additionally, you will be asked to submit a video of yourself teaching this lesson which will be peer reviewed.
Using the Discussion tab of this page talk amongst one another about some topics that lend themselves to using problem solving skills more than others. This should help to prepare you to determine what you will be writing and teaching your formal lesson on at the end of this unit. Please remember to use proper online etiquette and be respectful and formal in your postings and responses to your peers posts. The language used in these posts should be language that would be used in a discussion being conducted in a face-to-face environment.
Problem Solving Strategies
Survey, Question, Read
This method is a discussion based method where students and teacher go back and forth expanding on the problem at hand. This allows students to dig deeper into the meanings behind information in the problem that is being worked on. This allows that students to categorize information as important or extraneous in order
to find their way to the solution in a more effective and efficient manner. During the survey section of this method the students are reading and summarizing what the problem is telling them. The question section has students deterring what the problem is asking of them or what they are trying to find. Finally the read section is where the students will reread the problem if necessary to pinpoint the exact material that is necessary. This is the step where the students will begin step 2 of the problem solving method described in unit 1 which is when the plan is devised.
A mnemonic device is a tool in the form of an acronym that is intended to help a person to recall a topic. Some common examples of mnemonic devices that are used in the math classroom are "FOIL", "SohCahToa", "All Students Take Calculus", and there are many more. As you can see from the examples given this strategy can use letter strategies or sentence mnemonics. While this is not a complex problem solving strategy it can be helpful in supporting other strategies because it allows for students to have quickly be able to recall prior formulas or processes to solve a mathematical problem. Outside of the math classroom by using familiar terms to remember an unfamiliar concept.
Frayer Vocabulary Model
The Frayer Model is a strategy that is used for vocabulary construction. This is another strategy that can be used to support other problem strategies because it allows students to recall content specific vocabulary and apply it in the proper place and manner. This method draws on prior knowledge and allows students to make connections between different and seemingly unrelated topics. This strategy could be especially useful when working with proofs in order to better understand the relationships and meanings of different theorems, axioms, and postulates.
When using visualizations students are taking a problem that is in words and make some sort of pictorial version of a problem whether it is drawn out to represent the problem at hand or there are manipulatives that are used to represent that material in the problem. A good way to use this approach to solving a problem would be to have students read the problem and determine the important information (step 1 in the method described in Unit 1), then the students create the visual representation of the problem, finally the students can write their number sentence or equation and solve the given problem. Below are two videos which show teachers using visualizations to show students how to work through problems in a math classroom. After you watch the videos please go to Visualizations and share an example of a way that you have used visualizations in the past even if you used it incorrectly and example how it worked for you and if there was anything that you would change now that you are more informed. If you have never used visualizations please give and example of how you would use them in your classroom and why you would use it for the topic that you chose. (Note: The topic must be different than one of the topics presented in the video if you have never used visualizations.)
This method is a type of visual representation that show relationships between facts,ideas, or aspects of a situation (problem) that is intended to be used to guide the user's thinking. There are different types of graphic organizers one type is known as a Hierarchical Organizers which begin with a main idea and branch off with concepts related to the main idea an example of this being used would be the main idea to be the title of the unit and then for the branches are the individual lessons and then more branches representing the main ideas from each lesson. Another graphic organizer is a Venn Diagram which is used to compare and contrast, a common type of problem that would be aided by using a venn diagram would be a logic problem in order to help classify the information that is presented. A third example of a graphic organizer is a Four Square Organizer that is often used with the Frayer model as pictured above, as stated under the description of the Frayer Model this organizer would be useful for solving proofs. A fourth example of a graphic organizer is a KWL chart in which students fill in the columns of what they Know, what they Want to know, and what they Learned. This is a useful tool when solving almost any mathematical problem but especially word problems because the information can be classified, it forces students to determine what they are looking for, and it allows the students a space to justify their answer and how they came to their conclusion.
--Note: If students are unfamiliar with graphic organizers or the graphic organizer that you choose to have the students use for the problem they are trying to solve it is best to model the format using a familiar topic or problem rather than an unfamiliar one.--
Cooperative learning is a form of group work where students work together to reach a common goal. This strategy is useful for solving more complex problems, problem sets, or working on projects that combine numerous different problems. This environment allows students to communicate back and forth with one another analyzing different paths to reaching a solution and the students can work together to decide which pathway would be the best for the problem(s) the students are looking to solve. In order for this type of problem solving to work there needs to be a positive working relationship amongst the members of the group, each member must be accountable for their own work, there must be interaction amongst the members, and there must be a group processing where the group members discuss what they have to solve the problem, what they need to solve the problem, and what method will they use or not use and why. In this model the teacher is there to support group members, explain the task, and do all the behind the scenes work that goes into creating the groups and setting expectations for the groups.
If you know any additional strategies that have worked well for you in the past please share them Here so that all the participants in the class can share ideas and techniques that have been seen to be successful!
For this unit you will be expected to create a formal lesson plan using the template of your choice for the math subject and topic of your choice. This lesson must be aligned with Common Core State Standards, must include AT LEAST ONE of the above described problem solving strategies, and must be videotaped when taught to be submitted for peer evaluation. The rubric which you will be evaluated on for the lesson plan is below. When submitting your video please email the video to KBROOKS892@gmail.com and the instructor will forward it to the peer who will be evaluating you. The rubric which you will be using to evaluate your peers is below. When you are finished evaluating your peer's teaching please send me a completed rubric at KBROOKS892@gmail.com and I will send it to the participant after reviewing the evaluation. Part of your grade for this assignment is completing the peer evaluation.
- Effective Problem-Solving Instruction. (2014). Retrieved May 10, 2015, from http://raisingthebar.wested.org/resource/effective-problem-solving-instruction
- Exceptional Student Education. (2010). Retrieved May 10, 2015, from http://www.fldoe.org/ese
- Frayer, D.A., Frederick, W.C. & Klausmeier, H.J. (1969). A word is a word...or is it? Edited by M.F. Graves. 1985. New York: Scholastic.
- Leu, D. J., & Kinzer, C. K. (1991). Effective reading instruction, K-8 second edition. New York: Macmillan Publishing Company.
- Murphy, J. (2013, February 23). Graphics Organizers Help Students with Math. Retrieved May 13, 2015, from https://jackiemurphy21.wordpress.com/tag/graphic-organizer/
- Whicker, A. (2012). Visualizing Geometry. Retrieved May 10, 2015, from https://www.teachingchannel.org/videos/visualizing-geometry-lesson