My Research Paper on Fermat

Criteria for Implementing Flipped Instruction

This is from Ivan Hannel and can be found through ivan@k12workshops.com

 
Today's learners are in a unique and enviable position. Their universe of available knowledge is nearly unconstrained. The Internet gives them access to an immeasurable amount of information, instantly received at a very low cost or free. The educator in each of us sees the potential here to vastly accelerate student learning. Developing some criteria that may help to guide this transformation in terms of classroom instruction is a good starting point.

The "flipped classroom" is the moniker given to a construct for making better use of students' new and remarkable access to information. In the flipped classroom, direct instruction is the gambit of the home, while the classroom is the time for what we might call coached instruction or guided practice.

The basic idea is that the traditional stream of direct instruction-often a lecture--is reassigned to students as homework to be viewed via video or guided animation or podcast on the student's own time. The teacher then uses the next day's in-class time to coach students individually, ask and answer questions, conduct experiments, deepen the learning or otherwise do everything but lecture.

Until recently, high quality online lectures covering the grounds of K-12 education were hard to find. But websites like Kahn Academy and many others have tackled that ambitious task. You can find impressive videos on almost any strand of instruction you can think of.

As schools consider the flipped instruction model, what criteria might be used to determine what should be required of the direction instruction and the coaching component? Put another way, how do we know that the video is going to work for our students and what are we going to do after that? 

Because there is no definitive framework for the flipped classroom, feel free to amend or enhance these suggested criteria with ones of your own.

Direct Instruction

Below, I refer mostly to "video" as the format used in the direct instruction. But I do so just for the sake of convenience and recognize that the direct instruction may have many different formats. When thinking of the direction instruction, we should ask does the video?
__ Cover the content
The video must of course address the material described in the curriculum and do so in a way that is comprehensive and accurate.

__ Describe and organize the learning

Even if the information in the direct instruction is comprehensive, many videos don't frame the learning for the learner at the start. The author may assume the student "knows where they are." Does the author put things in context and tell the student what they are going to learn in the video and/or what is prerequisite?
__ Scaffold the concepts or skills to be learned
A video that covers the information in terms of the content but does not scaffold the actual learning during the video may not help the learner to actually learn. The content, concepts and underlying skills must be organized so that the learning builds up. This is essentially a question about ordering.

__ Allow for discussion amongst other learners
Learners often can help each other through forums. Is there a way for learners to ask and answer each other's questions on the same site where they receive the video?

__ Frame the learning in different ways
Does the author represent the information in different ways or perspectives? If there are multiple approaches to the content, does the author explain or address those alternatives?

__ Help the learner to self-assess
Some authors provide both the direct instruction and quizzes to help the learner know whether s/he has mastered the content at relevant times. Can the learner do a self-check for understanding?

__ Engage the learner
Ultimately, our hope is that the very best of direct instruction is what the student receives-the most interesting teacher teaching in the most interesting way. Will this author's video interest the student?

The Coaching instruction

The coaching instruction is the art of teaching. This is when the teacher actually works with students one-on-one to reinforce or hopefully enhance what was learned in the direct instruction. Because there are so many ways of doing this, from asking questions to creating experiments to dramatizing events to revising essays, there isn't a set of criteria to address every form of coaching. But there is one thing that should remain true of all coaching instruction: The teacher should strive to construct mediated learning experiences (MLE) with students during the coaching component.

The term MLE is attributed to Dr. Reuven Feuerstein of Israel, a psychologist, educator, and student of Jean Piaget. During an MLE, the role of the teacher is to stand between the learner and the underlying content and continually filter, frame, focus and guide the cognitive acts of the learner until he or she has reached understanding.

The teacher should:
___ Present himself or herself as exploring the content with rather than to the learner
___ Intend to teach not just the content but the underlying cognitive skills that underlie its acquisition
___ Help the learner evaluate his or her own learning
___ Bridge what was learned to other uses.

MLEs place a premium on the idea of engagement between teacher and learner rather than placing a primacy on the delivery of content itself. The opportunities for MLEs with the individual student are far fewer during a lecture, when the primary objective is often simply to present the content to all.

The flipped classroom thus places a premium on the capacity of teachers to create MLE's more so than being master-presenters of the underlying content. 

Creating MLEs is the part of teaching most congruent with our hope for individualized student learning. It allows lecture and other direct instruction to be outsourced to the proverbial Einstein's of lecture, while giving the classroom teacher time to bring his or her teaching skill to meet the immediate needs of the individual student.

The concept of the flipped classroom will be fleshed out over time. It will be most interesting to see how the incredible breadth of the Internet may be combined with the particular skills of teachers to enhance our students' educational futures.

Nine Dangerous Things You Were Taught In School

Originally from http://finance.yahoo.com/news/nine-dangerous-things-you-were-taught-in-school.html

Dangerous things you were taught in school:

1. The people in charge have all the answers.
That’s why they are so wealthy and happy and healthy and powerful—ask any teacher.

 

2. Learning ends when you leave the classroom.
Your fort building, trail forging, frog catching, friend making, game playing, and drawing won’t earn you any extra credit. Just watch TV.

[More from Forbes.com: The Six Enemies of Greatness (and Happiness)]

3. The best and brightest follow the rules.
You will be rewarded for your subordination, just not as much as your superiors, who, of course, have their own rules.

 

4. What the books say is always true.
Now go read your creationism chapter. There will be a test.

5. There is a very clear, single path to success.
It’s called college. Everyone can join the top 1% if they do well enough in school and ignore the basic math problem inherent in that idea.

[More from Forbes.com: Why Weird is Wonderful (and Bankable)]

6. Behaving yourself is as important as getting good marks.
Whistle-blowing, questioning the status quo, and thinking your own thoughts are no-nos. Be quiet and get back on the assembly line.

7. Standardized tests measure your value.
By value, I’m talking about future earning potential, not anything else that might have other kinds of value.

8. Days off are always more fun than sitting in the classroom.
You are trained from a young age to base your life around dribbles of allocated vacation. Be grateful for them.

[Related: Is Going to College Worth It?]

9. The purpose of your education is your future career.
And so you will be taught to be a good worker. You have to teach yourself how to be something more.

Integration and Geogebra

I gave the following as my integration unit exam.  I have to thank Bowman Dickson @bowmanimal, his blog is http://bowmandickson.com/, for giving me the instructions and project with the geogebra.  Below is the assignment as well as some of the pictures I recieved.

Integration Project

1.      Create an equation for the velocity of a particle at any time t, stating the initial position, which cannot equal 0.  The equation must include all of:

·         A polynomial function

·         Rational function –Chain rule must be applied

·         Trigonometric function

a.       Determine, using appropriate sums of rectangles, an over and under estimation of the displacement of the particle in the first 10 seconds.

                                                              i.      Explain how this estimation could be made more exact.

b.      Determine the exact displacement of the particle for the first 10 seconds, and then determine the exact location of the particle after 10 seconds.

c.       Determine the average acceleration of the particle from 0.  Illustrate how your answer could have been determined by the graphs.

2.      Complete a picture using geogebra with at least 5 areas calculated by hand.

Examples of the pictures

 And here is what one looks like after the lines are removed.

Instructions for Geogebra:

Calculus Speed trap

Catching speeders from our math class

Instead of using a worksheet, or pseudo-context question from a textbook you can show how related rates can be used to estimate the speed of a car from our classroom window.

1)      I used the Distmeasure app to determine the distance my classroom window is from the road.

2)      A student extended his arm and followed a car with arm until it hit a 45 degree angle.  Different students timed how long it took and we averaged the times.  [This will allow us to calculate the average rate of change of his arm in radians/second] in our class this took 4.6 seconds, as the following:

3)      Perform the calculations below

Since we know that student stopped at 45 degrees we can use the special triangle of 45/45/90 to substitute into the above formula.

We can then deduce that car is speeding through the school zone.

4)      Talk about the limitations of this activity, and how accurate this is.

Changing Assessment Presentation

I am putting on a session called "Globablization of Assessment" Below is my presentation and talking points:

Globalization of Assessment on Prezi

My Talking points:

Math teachers indicated that they rely on a textbook for more than 80% of their teaching and most math teachers (at least 60%) reported that their instruction is quite similar to textbook tests. – Center for the study of testing, evaluation, and education policy.

Mayor of New Jersey strongly backed the pedagogical approach of using “constant drill and repetition” and even said “It is not that hard to give answers if someone just told you what to say.  They memorize back and know and get used to a lot of A’s on quizzes”  But when asked if he would send his own children to this type of school, he answered “no, those schools are best only for certain children”.

Imagine the difference between your child running home and saying “I had a great day because I got an A, got the highest mark in the class, won the math challenge” or saying “I know understand how to reduce fractions, multiply two digit numbers, or argue critically”.  One is saying learning is a means while the other is regarding learning as an end.

Research has shown that an overemphasis on achievement:

1)      Undermines students interest in learning

2)      Makes failure overwhelming

3)      Leads students to avoid challenging themselves

4)      Reduces the quality of learning

5)      Invites students to think about how smart they are instead of how hard they tried.

When we get carried away with results, we wind up, paradoxically, with results that are less than ideal.  Evidence has shown that our ideal long term goals for our children and students are less likely to become reality when the education system and its stakeholders become preoccupied with standards and achievement.

If the point of school is to achieve and demonstrate success instead of stretch your thinking and be challenged, then it is completely logical that a child will always take the easiest route; sometimes the unethical easier route.

501 mothers were questioned and more preferred their children to complete projects that would involve less struggling but result in success than those where their children would learn a lot more, struggle through it, and could potentially make a lot of mistakes.  Is this right?

Candle project – rewards slowed down the thinking.

The probability of getting a reward has the same brain action as someone who is addicted to drugs.  Rewards promote just as much bad behaviour as good ones.

People of different abilities tend to learn more effectively on a range of tasks when they’re able to cooperate with one another than when they are trying to defeat one another.

Grades divert attention from education itself and otherwise prove counterproductive.  They also do not provide accurate and reliable information.

Interesting studies:

When teachers use hands-on interactive learning activities, students who were not graded at all did just as well on a proficiency exam as those who were.  Students who attended elementary schools where no grades were used matched a sample of students who had received traditional report cards for 6 years.  5^th graders who were told they would be graded on how well they remembered the social studies curriculum had more trouble understanding the main point of the text than did those who were told no grades will be used.  Even on strict recall the graded group remembered less.

Studies have shown over and over the more creative the task the worse of the performance of students when grades are used.  Only when comments are given, instead of numerical scores, will the learning increase.  Ruth Butler’s experiment

Tests and grades may make students learn today but will they may not want to tomorrow