Posted by David Wetzel
Active Learning
Active learning has a powerful impact on student learning. How? Student achievement increases through mastery of science and math content as a result of this technique. Students also develop improved problem solving, communication, and higher order thinking skills.
Before discussing the benefits of active learning, I need to establish a definition for this teaching technique.
“Students participate in teaching and learning beyond simply listening to lectures or witnessing demonstrations concerning science or math concepts.”
Four Principles: Basics of Active Learning
Four basic principles guide this teaching technique and stipulate that:
- learning is by nature an active process
- students learn in different ways
- students learning by doing
- use of higher order thinking skills by analyzing, synthesizing, and evaluating (Bloom’s Taxonomy or Bloom’s Revised Taxonomy) scientific or mathematic problems and findings
Benefits for Students: Advantages for Participating in Lessons
The advantages for student participation are grounded in the use of higher order thinking skills as students are more:
Focused – students are more attentive in class when they participate. Why? Few students actually listen to teacher lectures or demonstrations of how to solve math problems or explanations of science concepts – passive learning. However, their attention and focus are increased when students:
- question the importance of specific procedures for solving a math problem or data collection techniques in a scientific investigation.
- use the language of math or science as they communicate using correct terminology for explanations, asking questions, and responding to your questions. This helps them link terms with definitions.
- connect concepts and link big ideas in science or math during open class discussions.
- are more likely to complete homework or other assignments when they understand you will ask questions, using random student selection, regarding these assignments.
Engaged – achieved though stimulating student interest by causing conflict with their prior knowledge and experiences, along with assessing their understanding. This can be achieved as you ask higher order thinking open-ended questions, for example:
- What are the differences (or similarities) between …?
- How does … relate to what we have learned before about …?
- Explain why you agree or disagree about …?
Student Participation Techniques
Using time tested teaching techniques, along with the integration technology; students are more focused and engaged at all ability levels. Examples include:
Case Studies – groups defend or assail a point of view regarding a specific concept or idea. This approach is beyond simple knowledge, comprehension, or application of a concept. Students are required to analyze, synthesize, and evaluate evidence and use their findings to support their point of view. Examples include:
- Integrating Podcasts in Science and Math – student groups create a podcast of a specific potion of a unit or chapter studied in class. The podcasts are posted on a class blog or Wiki and are downloadable for students to use when studying for tests. Each podcast should be limited to five to six minutes to promote a clear and concise summary of key concepts, ideas, and problem solving.
Visual Webs – groups use concept maps, graphic organizers, or Venn diagrams to make connections between related concepts or ideas. Students construct their visual webs using Google Docs, Bubbl.us, Keynote, Power Point, Inspiration, Prezi, or Kidspiration.
Student Blogs – provide opportunity for students to participate in collective math or science problem solving. Students spend more time on accuracy and information provided when they are aware their classmates will provide input or feedback, not just their teacher.
Brainstorming – students contribute ideas as a collaborative process for providing possible solutions to problems or situations requiring analysis, synthesizing, or evaluation of findings or conclusions.
Active learning has its foundation in constructivist and inquiry-based teaching and learning techniques. The building blocks for these techniques involve active student participation by talking, listening, writing, reading, investigating, problem solving, and reflecting.
Your Turn
Of course these ideas, techniques, and strategies are only a beginning. Contributions to this discussion are welcomed.
Sources
Active Learning Techniques, Office of Instructional Consulting, School of Education, Indiana University Bloomington, 2010
Learning to Think, Thinking to Learn: Models and Strategies to Develop a Classroom Culture of Thinking, Pohl, M., 2000
Using Technology to Improve Student Achievement, North Central Regional Educational Laboratory, 2005
Posted by David Wetzel
Making Real World Connections with Algebra
Teaching Algebra is always a challenge with students, because it is procedural driven and typically taught without any connection to the real-world.
This is why students constantly ask - “I will never use this, so why do I need to learn it?”
This explanation - “You need to learn it, because algebra helps you develop logic thinking skills and employers expect you to have passed an algebra class in high school.” falls on students’ deaf ears.
Algebra needs to be taught in the context of real-life applications so students can develop a better understanding of why and where algebra is needed.
Real World Algebra Problems
Two sample real-world algebra problems are:
“If a batter goes into a game with a seasonal batting average of “S” after a total of “T” times at bat, and gets “K” hits in that game for “N” times at bat, the batters new batting average is determined by this expression:”
“Suppose a roller coaster ride begins by climbing to a height of 50 meters, and then falling rapidly to a height of 10 meters. If you ignore the effects of friction, then as it falls its velocity will be related to its height above the ground by this equation:”
Learning Variables, Patterns, and Functions
Variables is used in algebra for developing expressions and equations, because students need to determine what independent and dependent variables are, for example y = x.
This has real-world connections with science, since students must identify independent and dependent variables when conducting science experiments.
Lets take a look at a sample real-world problem in which students use variables to solve algebra problems.
High school algebra students are fascinated with getting their drivers license to experience the freedom of driving a car.
One thing they do not understand is center of gravity and the fact cars with a high center of gravity will turn over quickly when turning corners at a high rate of speed.
Note: Watch high school students peeling out of their school’s parking lot any day to observe this first hand.
Problem: Which car do you think is likely to roll over in a sharp turn?
Show students pictures of an SUV and sports car, when asking this question.
Then provide them with materials that represent the differences between these two types of cars (different size blocks of wood or cardboard boxes) for them to test.
In this real-world application, students are using algebra concepts related to patterns, functions, and variables.
Students should find the amount of force required to lift the opposite side of the vehicle depends on the width of the vehicle - the greater the width, the more force required.
Graphing the data should yield points which lie roughly on a straight line and pass through the origin (proportional function).
Students then determine the slope of the line to find the formula which describes the relationship - Force required = (slope) × width of vehicle.
Connections with Real-Life
When I took algebra in school, a long time ago, it was boring and I asked the same questions students ask today. All we did was work problems in class after the teacher demonstrated how to solve the problem on the board. I passed, although I hated every minute of algebra class.
Fast forward a couple of decades - Has anything changed? In most cases no! My children learned algebra the same way as I did, except this time they are completely turned off to mathematics.
When algebra is connected with real life situations, it gives students a personal connection. They can draw upon their prior knowledge and life experiences to help make these critical connections.
Everything else is evolving and changing, so should algebra continue to be taught the same way?
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Filed Under: Math
Posted by David Wetzel
Project Based Learning and Math
Estimates are about 80 percent of Math Education at the K-12 level is strictly focused on solving math problems without any real-world context (Computational Thinking and Math Maturity: Improving Math Education in K-8 Schools, Dave Moursund, 2007). Students’ math learning strategies are narrowly confined to written and mental skills, speed, and accuracy in solving problems.
The weakness of this approach is there is not enough emphasis on placing math problems within a real world context. This is often referred to as the root of students constantly complaining – “Why do I need to learn this, I will never use it!”
Math Teaching Framework
The following is a framework for teaching math for conceptual understanding and making real world connections.
- Math Problems – these comes in form of numerical and word problems for developing a reasonable level of speed and accuracy in performing addition, subtraction, multiplication, and division on integers, decimal fractions, and fractions. This also applies to knowledge of basic algebra, geometry, statistics, probability, and other higher math topics.
- Solving Math Problems – emphasis is on learning course material through rote memorization of steps and procedures in preparation for the next course. This strategy does not prepare students in developing the skills necessary to transfer new math knowledge and skills into other subject areas or into situations requiring the use of math outside the math classroom.
- Real World Math Problems – students need to be taught math is the foundation of product purchases, engineering, culinary arts, medical fields, sciences, geography, sports, and more real world applications.
- Solving Real World Math Problems – the ideal approach for integrating real world math into math classes is through the use of project based learning. Other titles for this type of teaching are problem based learning or inquiry based learning. Whatever you want to call it – students are solving basic math problems with the context of real world math.
Project Based Learning
For teachers new to project based learning, the following are recommendations for helping you integrate this strategy and helping students make math connections to real world applications.
- Start Small – do not try to completely reinvent your teaching strategies and techniques all at once. Integrate project based learning into one chapter per unit at a time. This will help you work out the kinks and become more comfortable in later units.
- Train Your Students – you will often find students may not be used to this style of teaching and learning. Just like you are transforming your teaching strategies, your students need to learn how to transform themselves into self-directed learners, presenters, and problems solvers.
- Use Interdisplinary Projects – work with teachers in other subject areas if possible to create and begin projects. This helps you in getting feedback from colleagues and also helps students make those all important connections outside the classroom.
For teachers who are veterans with project based learning integration, try using the following strategies:
- Mentorship – become a mentor for a colleague who is striking out into the world of project based learning. This helps you by becoming stronger in using this strategy and you also have the opportunity to gain insights into new project based learning activities through this collaboration.
- Technology – try integrating new technological tools, especially Web 2.0 tools, into your students’ projects. Other technology tools include the use of interactive whiteboards, global-positioning-system (GPS) devices, digital still cameras, video cameras, and associated editing equipment.
- Collaborative Projects – if projects do not currently rely on collaboration with other classrooms or schools, try a multi-classroom approach. This can be accomplished by contacting colleagues in your within your school, colleagues in classrooms in other schools in your district or state, or other classrooms in schools in other countries.
Using these strategies help your students make connections to the world outside their classroom and most importantly build bridges to higher levels of learning and math understanding.
The road in mathematics can take many paths; however, solving real world math problems must move beyond its current estimated of only 20 percent application in math today. This approach will alleviate the inherent weaknesses in mathematics teaching and learning today.
Additional Resources
6 Steps to Creating a Project Based Learning Activity
Project Based Learning - Chemistry or Physical Science
Pythagorean Theorem - Real World Context
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Filed Under: Math
