Learning can occur on a final exam

Historically, I would say that the least amount of learning occurs during exam week.  This year, however, I have tried to make this statement false through giving my students a new final exam.  When the first group presented, not only did I see, hear and was taught about unique examples of how to use calculus, I can actually say the group still LEARNED through the assessment. 

Below is a video of their PowerPoint presentation, which they used as well as supplemented with dialogue. 

After the presentation they opened the floor to me by giving me 10 minutes of questioning.  Most of the questions they answered swift and correctly, until I asked “Do all functions, on a closed interval, have an absolute maximum?” . Their answer was “Yes”.  Of course this is incorrect.

Now here is how the learning occurred… First I will address the traditional way of assessment:

If this was a traditional final exam, I would have marked this question wrong and moved on to the next question and continued marking.  These students would never have received any feedback, as in the past, I have yet to see many students come back to see WHAT they did incorrectly on a final exam.  These students would have then gone on to university/college with this false knowledge.

How it has changed this year…

I didn’t let this false information continue.  I then asked, “What if I told you, I could draw a function on a closed interval without an absolute maximum?”  The girls looked at each other with confused eyes, and pondered the idea.  After some passing minutes, one replied accusing me of a liar.  I wanted to ensure they didn't continue on with this false information, so I then asked, “Is there any kind of function that continues upward on forever?”.  One quickly answered, “WAIT! A function could have a vertical asymptote and therefore have no absolute maximum.  I guess you weren’t lying”, the other girl smiled and agreed. 

After this, I wanted to ensure they had a true understanding and therefore I asked, “Can a function, without any asymptotes, on a closed interval, not have an absolute maximum?”  The enlightenment has occurred!  Both girls whispered quietly, and then turned and replied “If the curve has an open point at the highest point, then it would not have an absolute maximum”.

Learning had occurred, and yet it was a final exam.

I continued with my questioning, which they answered correctly, and I am happy to say that this experience has been a success with the first group!

Exams last part 2

Why do we give exams?

After asking many teachers the top three answers that have been given are:

1)      “To assess, and find out actually what the students know” Rebuttal to this
2)      “If we don’t test it, the students won’t want to learn it”
3)      “Hold teachers accountable for their teaching`

Rebuttal to 2:

First, we need to understand that there is difference between learning and achievement.  For more click here. 

Second, if a student asks you, “Why do I have to learn this?” and your first or only response is “for the test”, then you are actually destroying any possible engagement.  People need to understand that learners don’t ask for the application to challenge the teacher, but actually want to understand the meaning behind the concept. 

If there truly is NO real life application then I would first advise you to contact those in charge of your mandated outcomes and ask them why you need to teach the specific outcome.  In the defense of the government, if they don’t know there is a problem, how can we expect them to find a solution?

Assuming that the outcome does have real life application, we should be focusing on the relevance and not the mindless repetition of the outcome.  Contrary to some popular belief, students do crave knowledge, but they need to be shown the “why” just as often as the “how”. 

For some outcomes this is an easy task, while for others I understand this can be quite difficult.  I, however, do believe that no matter how challenging it might be to show the “why”, the learning that will occur because of it, will make the journey worth taking. 

An exam should not be the reason anything is taught in a class.  “Teaching to the test” should be the equivalent of swearing in a classroom; something that should NEVER be done or even entertained.    I read the following, and became sick to my stomach!

Everything that has to do with the test has been given such a high priority, that there is no priority any more but that … The bottom line question comes down to, "Well, what’s going to help them do better on the test?" And if it’s not going to help them do better on the test, well, we don’t have time for that right now (Wright, 2002, p.10).

I would hope, that most agree, that the above statement is not one that teachers should be making.  If you believe, however, that a test is the only way students will learn, you are on your way to making the statement above.  I strongly encourage educators to allow students to find significance in given tasks, and you will start to see that your test no longer becomes the reason students want to learn.

Learning first, entertainment second. Technology in the classroom.

Lots of talk lately has been whether or not technology can improve student learning.  I believe, when used correctly, technology can drastically improve understanding of concepts .  Using the virtual world destroys the boundaries we encounter in the physical classroom.  In all fields of education, we need to start using all tools available and not just the "traditional" tools that were around when we were in high school. 

When my SmartBoard was first installed in my class, I truly believed I was utilizing technology to its full potential everyday, by writing my notes on the SmartBoard.  Sadly, I have then realized all I had in my classroom was a glorified whiteboard.  This then caused to me think, "Even though I might have technology in my class, unless I am using it in a way that requires that certain technology, I am not using it correctly".

How do we utilize such technology?  Below are apps described by "eSchoolNews", and what the sites claims to be the top 10 iPad, iPhone, or iTouch apps.  The list could go on and on, as more and more educational apps are created daily.   No matter what technology we use, however, we need to be aware that its use should be promoting student learning and not just for entertainment.

^[1]
Name: Word Lens
Best for: Language Classes
Cost: Free
Features: Instantly translates signage from one language to another through the camera application
How to Use: Language teachers can use this program for scavenger hunts
^[2]Name: Molecules
Best for: Science Classes
Cost: Free
Features: Allows users to view and manipulate three-dimensional models of different molecules
How to Use: Visual learners can see how protein molecules are composed and can download new molecules from the RCSB Protein Data Bank
^[3]Name: Blackboard Mobile Learn
Best for: Students and teachers whose campuses already use Blackboard
Cost: Free
Features: Course listings, organizations users are involved in as well as access to any readings
How to Use:Users can enroll in any classes or organizations that they have registered for and download any assignments there instructors have posted
Name: Today in History
Best for: History Classes
Cost: Free
Features: Lists notable events in history as well as important figures who were born or died on a specific date
How to Use:Use for trivia quizzes or facts of the day
^[4]Name: Math Ref Free
Best for: Math Classes
Cost: Free
Features: A free version of Math Ref, this app offers 600 out of over 1,300 formulas, figures, tips, and examples
How to Use: Use as a formula study guide or to view graphs of different equations
^[5]Name: PI83 Graphing Calculator
Best for: Math Classes
Cost: $0.99
Features: With over 100 math functions, the graphing calculator is a clone of the TI-83 without the $70 price tag
How to Use: Use in place of any calculator to input data, make graphs or matrices


^[6]Name: Star Walk
Best for: Astronomy Classes
Cost: $2.99
Features: An astral telescope; Star Walk adapts its view to wherever the user holds it up to, highlighting constellations and planets
How to Use: Use for guided tours of the night sky or to find the location of any specific astral objects
Name: Cram
Best for: Anyone in need of test prep
Cost: $3.99
Features: Both teachers and students can create flashcards and tests and import and share them with others
How to Use: Use to study for standardized tests or exams, or create study materials for students
^[7]Name: Essay Grader
Best for: Teachers pressed for time
Cost: $5.99
Features: Essay grader comes with a bank of pre-written comments and helps teachers cut down on grading time without writing the same comments over and over again by hand
How to Use: After assigning a grade, teachers can then eMail the grade sheet directly to the student or export it to the computer for editing and printing
Name: eClicker
Best for: Teachers looking for classroom feedback
Cost: $9.99
Features: Providing instant results, eClicker charts the class responses, showing which areas are understood and which need more work
How to Use: Students select a response to a question composed by the instructor and are then able to participate without fear of being wrong, since only the teacher views the results

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Real teaching first, real learning second

I was asked what is real teaching?

Here is my response:

Real teaching is allowing students to discover and create their own ideas in a classroom. It is no longer being told, provided or informed of information, but actually having students takes risks and venture down new "educational" roads towards a product they can call their own. Teachers should no longer be heralds of facts, but actually facilitators of learning. 

Support first, learned helplessness second

Few years ago when a student had a question in my class, I would tell them the answer.  Telling answers, providing solutions, and informing students was the way I would teach.  Recently I have realized, as a true educator, I should not be telling, providing, or informing, but in fact facilitating learners in my class.  I no longer want to be an instructor of information, but in fact a facilitator of education.

When we, as teachers, grab the pencil/pen from the students’ hands, or complete a task for a student we are perpetuating a single idea; “Learned helplessness”.  Learned helplessness is defined as:

a condition wherein a person believes that no matter how hard he or she tries, failure will result.

This condition is being enhanced by environments were tasks are completed for students.  Some educators will say “finishing the questions for the students need to be done, due to time constraints”.  However, constantly “finishing questions” is creating a condition in the students’ mind that they are incapable of thinking on their own.  They will start to actually believe that there are inadequate to achieve success in certain areas. 

This, unfortunately, will result with students becoming reluctant or even scared to complete challenging tasks.  To some, learned helplessness will appear as being lazy, or bored, but I truly believe that students crave reasonable expectations from others, and want to live up to these expectations.  Saying that, if we have great expectations from students we will witness great things, but if our expectations are low then consequently little learning will result.

Here are several tips for combating learned helplessness:

·         set high expectations for your students

·         let your students know that you see them as capable individuals

·         encourage your students to try it on their own

·         provide multiple opportunities for student trials

·         positively reinforce the student's efforts

·         if completing the entire task is not a possibility, encourage the student to complete the parts that he or she can do

·         encourage the student to try a bit more with each success

·         if you must complete a task due to time constraints, let the student know that he or she will be expected to do the task when time is not an issue

·         allow your students to see you struggle with a difficult task

Students need to be challenged, empowered, and congratulated, but not told, informed, or provided with answers.  Once students have the support, learned helplessness will be abolished.

Learning first, achievement second, homework still dead last.

I have received many responses to my "no homework" policy, so I decided to blog more about it.  In my classes, I do not assign daily required work.  I have, however, given my students assignments to complete out of class time, but these are not the traditional math assignments.

The myth about daily repetitive work is that this actually increases student mastery of a concept.  Many people believe the saying “Practice makes perfect”.  This saying, recently, has evolved to “perfect practice makes perfect”.  I would agree to the second statement when referring to a physical skill, such as shooting a basketball.  To master a physical skill, our body needs to mimic the correct actions multiple times.  The question that homework in a classroom does not address is “How does one practice understanding?”

Psychologist, Nate Kornell, completed a study that showed that intensive immersion is not the best way to master a particular concept.  Nate found that college students and adults of retirement age were better able to distinguish the painting styles of 12 unfamiliar artists after viewing mixed collections (assortments, including works from all 12) than after viewing a dozen works from one artist, all together, then moving on to the next painter.  Nate then deduced:

“What seems to be happening in this case is that the brain is picking up deeper patterns when seeing assortments of paintings; it’s picking up what’s similar and what’s different about them,”

Unfortunately, most classes immerse students into one concept; assign them multiple questions of the same concept, then move on to the next concept.  The research states that this is not the most effective way if we want students to retain mastery.

According to Cooper, homework increases student achievement (Even a formula has been created, 10 min per grad level)  This is a self-fulfilling prophecy.  First, educators need to realize that student achievement and student learning are not the same idea.  When looking at Cooper'sstudies, he shows that test scores increase due to the homework assigned.  Unfortunately, assigning repetitive work for students, or giving them loads of questions before an exam is the equivalent of cramming for an exam.

Cognitive scientists do not deny that cramming will lead to a better grade on an exam (thus increase student achievement), however this knowledge is quickly forgotten (student learning has decreased).  We, as educators, need to realize we are here to increase student learning first and student achievement second.