K-12 Teaching and Learning From the UNC School of Education

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From the education reference

problem solving
A method of learning in which students work to understand a problem, create and carry out a plan of action, and review, discuss and evaluate processes for problem resolution.
problem centered mathematics
Student-centered mathematics instruction that uses problem solving as a means to discovery of mathematical procedures and emphasizes real-world applications to mathematical concepts.
problem-based assessment
Based on a problem-solving or problem-posing educational model, problem-based assessment involves the presentation of a problem the student must solve.
problem-based learning
Model of instruction in which the teacher poses an authentic problem for student resolution. PBL may be one among many strategies in a classroom or an entire curricular and instructional approach. In the course of problem-solving, students work cooperatively in groups to learn content and skills related to real world problems. The teacher acts as a facilitator to learning.

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Student presentations in the problem-centered classroom
In Problem centered math, page 2.2
The video clip below shows students presenting their solutions to a math problem. The students worked on the problem in pairs, and several pairs of students used different methods to reach different results. A discussion results among the students as to the...
By Grayson Wheatley.
Story Problems Made Interesting
After introducing students to story problem strategies, students will be asked to write their own story problem(s). The problems must deal with real life situations. Fantasy worlds and silly situations are not allowed. Each student must also be able to solve their own problem(s). If the problems are not entered into a computer and saved, then the teacher will compile groups of problems for the students to solve. The author's name of each problem should be attached to the problem. If a student needs help solving a problem, he/she is only allowed to ask the author of that problem for assistance.
Format: lesson plan (grade 3 Mathematics)
By Tim Galliher.
Problem centered math
Why students must build their own understanding of mathematics if they are to be able to use it in the real world, and how teachers can guide them in doing so.
Format: series (multiple pages)
Building a paper bridge: An introduction to problem solving
This activity allows the student to explore problem solving strategies while working with a partner. This activity (building a paper bridge), requires students to question word definition and the application of those definitions. Through problem solving strategies, students discover the need for applying math skills.
Format: lesson plan (grade 8 Mathematics)
By Steve Walston.
Math for multiple intelligences
How a middle-school math teacher realized she was boring and jump-started her career — and her students — by using thematic planning, emphasizing problem solving, and teaching to multiple intelligences.
Format: series (multiple pages)
Ecosystem problem solving
Students will apply their knowledge of ecosystems and the interdependence of plants and animals to creatively solve problems.
Format: lesson plan (grade 5 Science)
By Kelley Turner.
Algebra for the real world
Students will solve real world and mathematical problem situations using simple algebraic concepts including variables and open sentences.
Format: lesson plan (grade 4–5 Mathematics)
Solving workplace problems: Refining the use of argument
In CareerStart lessons: Grade eight, page 1.8
In this lesson plan, students are presented with two writing prompts that describe workplace problems. Students complete a graphic organizer to help them map out the problem-solving process.
Format: lesson plan (grade 8 English Language Arts and Guidance)
By Andrea Fedon, Gail Frank, and Cindy Neininger.
Solving problems, writing solutions
In CareerStart lessons: Grade six, page 1.5
In this lesson for grade 6, students consider problems in the workplace and follow writing prompts to craft solutions.
Format: lesson plan (grade 6–8 English Language Arts and Guidance)
By Jennifer Brookshire and Julie McCann.
Problem solving with Swimmy
This lesson will stress to the students the importance of working together to solve a problem.
Format: lesson plan (grade K–5 Guidance and Healthful Living)
By Amy Taylor.
Reindeer boots
Children will use problem-solving techniques to answer the question, “How many boots will Santa need for his reindeer?”
Format: lesson plan (grade K–1 Mathematics)
By Vanette Hann.
Problem-solving careers
In CareerStart lessons: Grade seven, page 1.7
In this lesson for grade seven, students analyze information about various careers to determine how people in those occupations use problem-solving skills.
Format: lesson plan (grade 6–8 English Language Arts and Guidance)
By Jen Presley.Adapted by Kenyatta Bennett and Sonya Rexrode.
Rocket launch
Students will work individually and in collaborative pairs or groups to solve a rocket-launch problem. The pairs/groups will then present potential solutions to the class for discussion. Similar problems will then be solved and created by students.
Format: lesson plan (grade 4–5 Mathematics)
By Ron Hann.
Topics in Mathematics Education
In Preservice teacher education resources, page 4.2
Resources Specific to Math Math Teaching Methods Numbered Heads Together Numbered heads together is a cooperative strategy that offers an...
Format: article/teacher's guide
Design technology: Children's engineering
This unit includes design technology projects linked to major themes in engineering. All the lessons and activities support national and state standards. They include materials lists, procedures, student data sheets, and assessment strategies. The lessons vary in grade level and can be modified up or down.
Format: lesson plan (multiple pages)
Why problem-centered learning?
The world our students will live and work in will require them to gather, organize, and interpret data in the process of finding solutions to complex problems. Problem-centered learning creates a model where the student becomes the thinker.
Format: article
By Mike Kestner.
Crossed up hundreds board
Students will experience patterns and problem solving on the Hundreds Board.
Format: lesson plan (grade 3–4 Mathematics)
By Karen Bartlett.
Percent problem solving
Students apply their knowledge of fractions, decimals, and percents to understand the relationship amongst the three. Students will solve basic percent number problems using the percent proportion or other methods and play a game using a resource of the Shodor Education Foundation, Inc. Permission has been granted to use the materials as part of the Interactivate Your Bored Math Students workshop. Students will also analyze and explain the results of their game by answering two exploration questions.
Format: lesson plan (grade 6–7 Mathematics)
By Victoria Lunetta.
Take action, save the past
In Intrigue of the Past, page 5.8
In their study of archaeological resource conservation, students will use a problem-solving model to identify a problem and solve it creatively.
Format: lesson plan (grade 8 English Language Arts and Social Studies)
The problem-centered classroom
In Problem centered math, page 2.1
A look inside an eighth-grade classroom in which students work in pairs to solve problems, then debate as a class which solution is correct or easiest. An explanation of the teaching method is provided along with video of students presenting their solutions to problems.
Format: article
By Grayson Wheatley.