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Tristen Lechner

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(Manipulative/Observant)

Active learning is when students learn in a natural way and adapt to the environment they are surrounded by.  Students learn in this way by manipulating objects in their environment and observing the happenings that occur around them.  By manipulating objects around them, students then interpret these findings by observing their manipulations (basically a trial and error approach).

Example:
In 5th grade math, the students would already know how to add, subtract, multiply, and divide from previous courses.  Then there would come a time to incorporate decimals into the mix using these operations.  In teaching a lesson, I would use the base ten blocks to show the students how to  convert these manipulatives into whole numbers, tenths, and hundredths.  Then I would give the students a few problems on the board for them to demonstrate how to manipulate the base ten blocks to represent adding and subtracting decimals.

This image was taken from the following website that utilizes the problem as an example:
http://www.coolmath.com/prealgebra/02-decimals/06-decimals-adding-01

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(Articulative/Reflective)

Constructive learning goes hand in hand with active learning.  In constructive learning students need to make sense of their experiences because the outcome isn't always what one would anticipate.  When the students get results that they weren't expecting, that is when the learning process begins and the student is eager to find out why the outcome became a reality.  Then is another important task the students need to complete, reflection.  In the reflection process the students try to prove how and why their outcome happened.

Example:
In 5th grade math, after the students would get the hang of using addition and subtraction with decimals, I would introduce multiplying decimals.  The students may not understand how to place the decimal when multiplying decimals as it is different from adding and subtracting.  The students would anticipate the decimal just be brought down but in reality they would need to figure out why and how the decimal should be placed.

This image was taken from a website explaining how to multiply when using decimals:
https://www.google.com/imgres?imgurl=http://www.math.com/school/subject1/images/S1U1L5GL.gif&imgrefurl=http://www.math.com/school/subject1/lessons/S1U1L5GL.html&h=171&w=250&tbnid=v3kl_G_0FJPg4M:&tbnh=136&tbnw=200&usg=__1VpMvhr1RyX4JJoGWEi8xg3XZA8=&vet=10ahUKEwiZnLHtpajUAhUD34MKHZoGAXcQ9QEIJjAA..i&docid=PDg3fJAD5QB_RM&sa=X&sqi=2&ved=0ahUKEwiZnLHtpajUAhUD34MKHZoGAXcQ9QEIJjAA

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(Reflective/Regulatory)

Intentional learning occurs when students want or need to learn something on purpose to accomplish a goal.  Students have proven to think and learn more when they do it with the intention of learning on purpose to obtain a goal of some sort.

Example:
In 5th grade math, after teaching the adding, subtracting, and multiplying using decimals some of the students would create a goal for themselves to try and figure out how they could divide decimals.  Many of the students would anticipate this to be the next lesson, so many of them would go ahead and try to come up with how to divide decimals on their own.  This is a great way of the students taking the initiative to create a goal and figure it out on their own.

This image was taken from a website showing how to divide decimals:
https://www.google.com/imgres?imgurl=http://www.math.com/school/subject1/images/S1U1L6GLe.gif&imgrefurl=http://www.math.com/school/subject1/lessons/S1U1L6GL.html&h=255&w=151&tbnid=vanm1bKINFzcqM:&tbnh=160&tbnw=94&usg=__3-MdTUJXu8hLYZx7nhuGdOYuxiY=&vet=10ahUKEwjduOzVp6jUAhVF6IMKHWuQAXcQ9QEIJjAA..i&docid=shZ0lC2l7cMH5M&sa=X&sqi=2&ved=0ahUKEwjduOzVp6jUAhVF6IMKHWuQAXcQ9QEIJjAA

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(Complex/Contextualized)

Authentic learning happens when teachers relate lessons to real-world problems the students can then relate to.  It is important for teachers to think outside the box and let the students create and show how learning simple tasks can relate to the real world.  When learning is authentic it is more likely to stick with the student rather than telling the student to memorize and recall different items across the curriculum.

Example:
In another 5th grade math lesson, after the students completed the previous lessons.  On the smart board, I would write a few different decimal numbers down and ask the students to come up with two different places/reasons they have had an encounter with a decimal.  (This would gear them towards talking about money and how money amounts are decimals).

This image was taken from a website showing an example of a decimal number I could use to write on the smart board:
http://www.coolmath.com/sites/cmat/files/images/decimals01-4.gif

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(Collaborative/Conversational)

Cooperative learning is important to understand how to work with others and truly understanding your own personal strengths and weaknesses.  Throughout cooperative learning, while working in groups it is nice to use your group members strengths to make up for your own weaknesses and vice versa.  This allows the group to capitalize on each persons individual strength and contribute it towards one goal in a group.  Students don't learn anything if you place them into groups and let one person do all the work in the groups.  It is important to hold each student accountable both individually and as a group member.

Example:
For the final 5th grade math lesson, I would assign the students into groups of 3-4 students.  In these groups the students would need to work together to complete a "virtual field trip to the zoo".  This would include completing a worksheet using decimal values to attend the zoo and also holding the students responsible for showing their work to add, subtract, multiply, and divide decimals.  They would do this by answering story problems relating to the zoo.  Each student would complete their own worksheet (as a group), this would encourage students to have conversations as to how they should answer the problems.  I would also give them a peer feedback rubric to discuss how they felt each group member contributed to their group as a whole.

This image would be an example of a rubric I would use to evaluate the group members based on feedback within their groups:
https://image.slidesharecdn.com/4zcwzrmiru5b6r6qsobd-signature-e21f6464e84ff49f1a7edcdabde3903ed3896c43a7544fd60ed8331c3306f457-poli-150104164829-conversion-gate01/95/groupwork-rubric-1-638.jpg?cb=1420390256