Math Notes
Flipping a classroom is not a teaching technique, it is more in line with a philosophy or way of teaching. It involves using technology as a tool, not the main focus, for helping students increase their understanding of science or math concepts.
Effective use of this way of thinking helps reduce student anxiety and frustration when studying science or math, especially when homework is involved. Unfortunately, failure to complete homework is a common problem among students, because they typically work in isolation.
This aggravation causes students to view homework as a maddening waste of time — leading to incomplete assignments and ultimately poor grades as they fall further and further behind.
Contrary to perceptions some may have about flipping a classroom, homework is not eliminated. It uses an entirely different approach (Learning 4 Mastery, Student Impressions).
How does Homework Change?
Homework becomes a series of shortinstructional videos, teacher lecture screencasts, and podcasts on your blog or wiki designed to replace in-class lectures.
Why is this a good thing?
Lecturing Does Not = Learning
Have you ever experienced the glazed look in your students’ eyes when lecturing?
Do you observe them taking copious notes and not really paying attention to you as you talk or place notes for them to copy on the overhead, chalk board, whiteboard, or smart board?
Also, this delivery method provides students limited time to make sense and formulate questions regarding new information, i.e., they do not have time to assimilate the information or make connections.
Impact of Lecturing
Lectures result in a one-way transfer of knowledge that does not pass through your students brains. It goes straight from your mouth or screen to their pen or pencil onto paper — passing go (the brain), proceeding directly to a potentially never opened notebook.
Through your best efforts to teach the important concept(s) in a lesson, they have learned little and typically cannot apply the information. This is why traditional home work is frustrating and viewed as a waste of time by most students. Typically, students do not remember enough from class to complete their homework assignments.
Impact on Homework
Using the flipped philosophy, students learn from podcasts, lectures, or videos at their own pace. Also, they can review them as many times as want. Of course questions will come up, even higher-order questions. Why? Because students now have time to think about what they are observing — this is a good thing. Now lectures and content videos are passing through your student brains! Homework is now useful and a beginning point for the next day’s class.
Science Investigation
Homework Resources
The following is a short list of vieo resources for science and math.
- Kahn Academy an extensive list of short videos of science and math concepts and procedures.
How Does In-Class Time Change?
Classes now become a center for student learning. You have more time to interact with students on a one-to-on basis. Additionally,:
- you address student higher-order questions concerning homework.
- your opportunity to discover student misconceptions and procedural confusion is increased.
- students spend more time on experiments and investigations.
- students work in groups or independently to solve problems.
- you can differentiate instruction as necessary.
Flipping Your Classroom: Things to Consider
Is this for you and your students? Think about the following, remembering that like anything new it takes time and should be implemented in steps to avoid frustrating yourself and students. A flipped classroom is:
- not a substitute for you.
- a place where you are no longer the purveyor (one way communication) of all knowledge.
- a place where content is stored on your blog or wiki for student review prior to tests and absent or home bound students can review.
Challenging the Status Quo
Why use this strategy? Because in far too many cases the status quo is not working.
Although there are a multitude of reasons why students drop out of school, the process begins as early as elementary school. The leading cause is poor grades and test scores. Students do not feel engaged in school and find it monotonous (California Dropout Research Project).
Sources
California Dropout Research Project, UC Santa Barbara, Gevirtz Graduate School of Education, 2008
Learning 4 Mystery, Flipped/Mastery Educational Model: Student Impressions, Accessed December 12, 2011
Should You Flip Your Classroom? Edutopia, October 26, 2011
The White House, President Obama Announces Steps to Reduce Dropout Rate, Office of the Press Secretary, 2010
David’s Google +
Hands-On Learning Using Math and Science
Your students’ future and education needs are not like yours and mine. For the most part, we are a product of an education system heavily influenced by the industrial age – lectures and rote memorization. This style of teaching was primarily designed to produce factory and skilled trade workers.
Due to the dynamics of today’s world economy, most students no longer have the same types of jobs waiting for them when they graduate. Their future is in the service, health, and technology career fields. However, there is still a demand for skilled trade workers (Bureau of Labor Statistics, 2010).
A Need for a Shift in Teaching Strategies
Today’s education system is still following the demands of the industrial age. So how does this clash with students’ needs for the future?
When students are forced to sit in straight rows and listen to the industrial revolution style of teaching — lectures and rote memorization of facts — countless become bored underachievers! Primarily because education system is out of step with the information age.
Unfortunately, many students view math and science as the two hardest subjects to master. Why? Because there is way too much emphasis on lectures and memorization. This contributes to their boredom in school and does motivate them to learn.
So what must be done to stimulate their curiosity and engagement in a manner that makes them to want to learn math and science?
Tips for Increasing Student Engagement
Motivating underachieving students requires moving away from demonstration, telling, showing, and rote recall. Today’s math and science students need hands-on, minds-on experiences to stimulate and challenge them to think. The following are example strategies.
Technology Tools – must have specific learning objectives, along with real-world applications. Students use technology tools every day, so why not use their prior knowledge and experiences with these tools to challenge them to learn concepts.
Online Interactive Math or Science Programs – must address specific learning concepts. Not just means of keeping students occupied or as a reward for good behavior.
Problem Solving - solving real world problems frequently motivate underachieving students. Why? Because they are allowed to think out of the box to solve problems. Also, this strategy takes advantage of challenging higher-order thinking skills. This strategy works well for all students, not just underachievers. In addition, many students do not understand how to solve problems. These students must be taught how to solve problems.
Concepts – help students understand the critical features of a concept. This includes requiring students to develop examples and non-examples of a concept, assessing their true level of understanding. Also, require them to provide examples of a concept linked to one or more other concepts.
Lessons – must include opportunities for students to shift to a new, although still related to lesson objective, activity every 15 to 20 minutes. Examples include giving students opportunities to analyze, use or demonstrate what they learned, and show how to or explain what would happen if… This paradigm moves beyond completing worksheets (which in my experience, students view as busy work).
Higher Order Thinking (HOT) – requires the use of higher-order thinking questions. Open-ended questions to stimulate discussion. Do not use “yes or no answer” questions. Effective use of wait time “I” and “II.” Do not use questions which contain the answer. Example higher-order thinking questions, include:
- What might happen if ____?
- Can you summarize ____?
- What evidence supports ____?
- How is this similar or different to ____?
- How might you organize ____ into categories?
- What other ways can you show or illustrate ____?
Math Example
Instead of showing your students the formula in geometry for determining the volume of an object, labeling variables, and how to solve the equation. Followed by endless drill and practice. Give them concrete and tangible objects to explore, touch, and measure. This leads to higher levels of thinking as they analyze and apply the concept of volume. After providing them with a variety of objects (regular and irregular shapes), ask them how they will determine the volume of these objects. Example higher-level questions include:
- Which object has the greatest volume?
- How do you know this true?
- How many ways are there to determine the volume of an object?
- How could you visually represent your solution? (looking for a graph, table, equation, pictures, etc.)
Science Example
Instead of showing, demonstrating, or watching a video of a discrepant event. Allow students to participant through hands-on discrepant event investigations. For example: Air Pressure Materials – One Set for Each Group: one aluminum pan pie (non-smooth bottom), water, one 16oz clear glass, one candle (about 3 inches tall), and matches.
- Students attach the candle to the center, bottom of the pie pan.
- Now they pour water into the pie pan, about three quarters of an inch deep.
- Students light the candle.
- Now they place glass over the candle and observe what happens.
- Allow students to repeat as necessary.
After they have observed and recorded their observations, ask them higher-level science questions, for example:
- Why is ____ happening?
- What do you think is causing ____?
- You seem to be assuming that ____?
- What conclusions may be draw from ____?
- How is ____ different (like) ____?
Motivating underachieving students to learn math and science can be difficult or even challenging on occasions. With these teaching strategies students will no longer be bored by traditional lessons. They will find that math and science are not that difficult, because they are allowed to participate, think outside the box, and make connections.
Now it is your turn, do you have any additions to these strategies?
Sources
Occupations with the Largest Job Growth, Bureau of Labor Statistics, December 08, 2010.
HOT Skills Question Templates, Russellville Science Department Professional Learning Community
Critical Thinking
Encouraging students to use critical thinking is more than an extension activity in science and math lessons, it is the basis of true learning.
Teaching students how to think critically helps them move beyond basic comprehension and rote memorization. They shift to a new level of increased awareness when calculating, analyzing, problem solving, and evaluating.
Another way to view the power of critical thinking – as students learn how to apply and use higher order thinking skills, they learn how to question the accuracy of their solutions and findings.
Students wonder why they got the results they did and not another outcome. This in turn leads to internalization of concepts, along with all important point of making connections with related concepts.
Teaching Critical Thinking
Some students have the natural ability to ask higher cognitive questions. Specifically when evaluating experimental findings in science or solving math problems. However, many students do not have this innate skill and need to learn how to ask higher order questions.
An important point for encouraging students to use critical thinking is by modeling these skills for your students. Students will inherently follow their teacher’s lead; this is why it is important to practice what we preach.
The following are examples of questions to ask your students to encourage them to think critically (Richard Paul).
Probing
- What additional information do you need to solve the problem?
- How does the data relate to your findings?
- How does the evidence support your conclusions?
- What would you need to do to determine if the solution is true?
- How can you compare this with other problems?
- Are their alternative solutions to the problem? If so, what are they?
- What else may be true if this is correct?
- What effect would _______ have?
- What do you mean by that statement?
Implication
- How could you ask that question differently?
- What did you learn from solving this problem?
- Is this the most important question to ask when solving the problem?
- What questions need to be answered before answering this question?
These questions all have one purpose – keeping the train on the track by guiding students through the critical thinking process. When you ask these and similar questions, you are encouraging your students to move from passive to active learning.
Avoiding Questions Easily Answered on the Internet
Questions and problems easily answered through a quick query on the internet are not an effective strategy for teaching critical thinking. Students need questions which require them to create a product to show what they learned. The following examples are referred to “Google-Proofing” in some circles.
- Construct a data table and graph to display a comparison of cost of three competing cell phone companies.
- Design an investigation to determine the best materials for building a hurricane proof house.
- Compare the organs in the human body with other mammals.
- Create a board game based on geometric shapes.
- Redesign an existing product to reduce its carbon footprint.
The goal is to help students learn how to develop higher level questions and make connections when solving math problems or analyzing experimental data.
Quality Thinking In order to support quality critical thinking, the frequency of questions is not as important as the quality of questions. Also, increasing wait-time between teacher-student-teacher is important to success with teaching quality thinking. According to Kathleen Cotton, the following are factors to consider when asking students questions.
- The average level of questions asked by teachers are 60 percent lower cognitive, 20 percent procedural, and 20 percent higher cognitive.
- Increasing the frequency of higher cognitive questions to the 50 percent level produces superior gains in middle and high school student achievement.
- Asking higher cognitive questions does not reduce student achievement on lower cognitive questions.
- With predominate use of lower cognitive questions; students tend toward lower achievement.
The use of higher cognitive questions tends to elicit longer student answers in complete sentences, quality inference and conjecture by students, and the forming of higher level questions. This in turn results in increased student use of critical thinking and classroom participation. There is never a wrong time to begin encouraging your students to use critical thinking skills, so why not start today.
Sources
Cotton, Kathleen, Classroom Questioning, North West Regional Educational Laboratory.
Paul, Richard, Critical Thinking: How to Prepare Students for a Rapidly Changing World, Foundation for Critical Thinking.
The Best Resources in Teaching & Learning Critical Thinking in the Classroom
