Increasing Positive Emotion in Math.

 If you read the blog the other day, you'll know that our brains remember more if they have an emotional attachment to the material.  Unfortunately, too many students have negative emotional connections associated with math which creates several problems.

First, many people believe they are not good at math and will never get good at it so they have a mental barrier to learning.


Secondly, if a student does not like math, they are more likely to have lower achievement scores and as soon as they can, they quit taking math or are more likely to take lower level math classes.  This means they are closing themselves to certain career opportunities, especial those of higher earning potential.  It also limits how they will interact with society and it's possibilities.

Right now, if a student struggles with math, one of two things happen.  They are encouraged to work harder or they are moved into a lower level of mathematics.  Unfortunately, neither of these solutions may not help improve student attitude.

So the question becomes, what can we do as teachers to make class more emotionally engaging so students have getter emotional associations with math?  There are ways to do this, some work better with younger students, some with older students but all can help students associate happier emotion with math.

1.  Create authentic inquiry by setting up a situation where students can ask the questions.  It might be drawing a rectangular prism on the board and have students create questions the can be answered from looking at the drawing.  This makes the students operate more as real life mathematicians who guess, question, and narrow their solutions based on repeated results.

2. Always show more than one way to do the math but don't be afraid of asking students to see if they can figure out a way to solve the problem on their own.  This gives them a chance to find counter examples on their own, or set conjectures.  In addition, it motivates students and allows them to develop mathematical creativity.

3. Instead of having students sit in one place the whole period, create opportunities for them to move around.  It could be as simple as asking a multiple choice question, assigning one answer per corner and having students go to the corner they think represents the correct answer.  Or organize a scavenger hunt with at least ten half sheets folded in half.  On the front, write a problem, and on the second page, write an answer but it is not the answer to the problem on the front.  It is the answer to another problem.  These are hung around the room after assigning a letter to each problem. Students have a sheet with boxes.  In the corner of each box is a smaller box where they write the letter of the problem.   The idea is that students start at one paper where they write down the problem, solve it, and then look for the answer.  Once they find the answer they look at the new problem, write it down and it's letter in the box, solve it and repeat it.   I've been known to use QR codes with a problem and answer contained in the code so it uses student devices but they still write the problems down on paper.

4.  When you create an assignment, quiz, or test, set them up so students can choose the problems they want to do.  For instance, you might want to write a quiz with 15 problems and have students answer any 10 problems.  This increases student motivation and makes them feel as if they have some control.

5. Place both examples and non examples on the board before asking students to figure out what makes the topic.  For instance, when discussing spheres, one might post pictures of basketballs, baseballs, or an orange.  For non examples, you could post pictures of bananas, footballs, or boxes.  Let the students use this information to create a list of what characteristics a sphere has.

6. Establish situations where students can collaborate together in a learning environment.  For instance, you can set up Jigsaw activities for sharing vocabulary, create a slide show or book using google slides to have small groups of people share their material with others.

When math becomes more engaging and students feel as if they are taking over more of their learning, they develop positive emotions so they learn the math.  Let me know what you think, I'd love to hear.  Have a great day.  I'll be back Monday with a new topic but I will continue to post warm-ups.

Reading and Vocabulary.

I have recently started doing things differently in my Geometry classes because I'm trying to make students more self sufficient and make the class a bit more student centered. I need to teach a bit less while making the students more independent.

One of the first things I did was create a paper filled with a table of 16 squares.  In each square I wrote one of the vocabulary words for the chapter and nothing else.  I divided the students into small groups of two to three people depending on the size of the class.

Once I passed out the vocabulary sheet, I assigned three words to each group so no other group had the word.  I gave them time to work on defining the terms using their own words. One girl asked if they could draw pictures to help define the word.  I said go ahead because research shows it helps to have pictures to go with words.

After about 10 minutes, I had students get up to new groups so everyone in the group had defined different words.  They shared their vocabulary words with the others so by the end of the time, every person in the group had shared their words and had a chance to fill in all the other vocabulary words.  This is a variation on the Jigsaw activity.

What I liked was the variety of methods used to complete the assignment.  Some groups split the words up so one person defined a word before sharing it with the rest of their group so everyone had their three words defined before sharing with the other groups.  Others looked the words up together, discussed what the definition should be before agreeing on one.

The important thing with this activity is that the words are ones they've used before in their two column proofs so these words are not new but they've not had time to really look at the words in detail.  By waiting this long before doing a serious vocabulary activity, students had a chance to build prior knowledge.

The other thing I've started doing is again dividing students up into small groups and having them read the new material.  After they complete the reading, they have to decide what the three most important ideas or concepts contained in the material.  At the end, I asked each group to give me the one concept they thought was the most important and they had to explain their thinking.

I do this activity on one day and give them 24 hours before taking it to the next step because it gives their brain a chance to process the information.  One day later, I go back and ask them to prepare a more detailed explanation of that concept to share with other students.  This presentation can be done via google slides, a short video, or some sort of animation but they have to explain the concept and why it is important.

I've found that most groups came up with different choices so there is very little overlap.  If I do have two groups choosing the same topic, I often ask one group to think about why a certain other topic is important.  Most of the time, they don't mind the change of topic because it was one on their list of the top three.

Both of these activities encourage dialogue, communication, and explanations so they learn to discuss and communicate math.  I would love to hear what you all think.  Let me know, have a great day and I'll be back with something new on Friday.

Emotions and Teaching Math

We all have those students, the ones who arrive in your math class, convinced they can't do math or don't try because they see no use for it.  They have a negative emotional connection with math which can slow down their learning.  There are ways to help students gain better emotional connections.

Remember, emotions help us think because they pull up memories we have associated emotions with.  The question is then, how do we take advantage of this in our classes.

One thing we are told is to make math fun by incorporating games and prizes but these are considered a quick fix.  What works better is to help students develop a sense of accomplishment by making math interesting, satisfying, and personally fulfilling.  There are some steps each teacher can take to change student dislike into appreciation and wonder.

First, rather than letting students see math as some sort of torture to be tolerated until the math requirement is met, we should explain why these math concepts matter.  Mathematics helps students think both theoretically and logically.  Furthermore, math helps the brain think abstractly which is a skill that can be used in so many different ways.  There is research that indicates students who study complex math topics tend to do better in life.

Second, give students problems where they see how math is used in real life.  If they see connections, they are more likely to participate.  Practical applications range from keep track of their finances, to how fast oil spreads on tissue paper which gives students a real life application of direct variation and understanding of how fast oil spills spread.  Find stories in the news where a need to understand math is important such as in a story on price fixing, or climbing interest rates.  If you have students read an article on climbing. interest rates before setting up a spread sheet to show how much an increase of one-eighth of a precedent can effect the overall amount of money paid on a lone.

Third, take time to discuss mathematicians who helped change the world or make changes to the world such as Pythagorus, Rene Descartes, or people like Alan Turing who helped break Axis codes and allowed the Allies to win the war.  For the sports minded, introduce them to Nate Silver who uses statistical analysis to predict winners in elections and Major League Baseball.

Finally, look at ways to decrease the stress students feel when learning new material or taking tests.  When introducing new material, always try to relate it to previously learned material such as when solving one and two step inequalities, we can related the processes back to solving one and two step equations.  Relating it back to previously learned material also helps students learn the same material better or even get it when they didn't get it the first time.

This is an introduction to the topic.  I will be exploring it in more detail as I have a few students who see absolutely no reason to learn math and do their best to disrupt instruction so others have difficulty learning.  I want ideas to counter this "If I don't want to learn math, why should you?"  Knowing how emotion impacts learning is my first step to countering this.

I am slowing down to three topics a week plus warm-ups on the weekend because of the number of sports events happening at school.  I have been helping out and will continue to do so but it is not leaving me as much time for me.  So the next time I add new material, will be on Wednesday.

Let me know what you think about today's topic, I'd love to hear.  Have a great day.

Warm-up

Write a compound inequality to describe the situation.

Warm-up

Write a compound inequality to fit the situation.

Emotion and Memory

Did you know that emotions help your memory remember information?  Emotion plays an important part in how we remember things.

In general, emotions highlight certain parts of our experiences to make them more memorable.  It works in so many ways with our memories.  Some may be new to you, some may not.

First is attention which helps our minds determine what is most important in our lives.  Emotions such as novelty or surprise, helps us focus on conversations so we are aware of a few items which allows to use our limited attention span to its optimum.

Second is consolidation of memories.  The truth is that most of the information we are exposed to, do not make it into our long term memory.  When we have an emotional connection to something, we are more likely to remember it. For instance, most people of a certain age can tell you about 9/11 because of the emotions it brought up in everyone.  This is because certain stress hormones such as cortisol and epinephrine help us consolidate our memories.

Thirdly, it appears that those memories associated with painful events stay with us longer than memories associated with physical pain.  Contrary to the rhyme about "sticks and stones may break my bones but words will never hurt me" we do remember the words that hurt us.

Next is priming or triggering behavior through the use of unconscious suggestions.  For instance, if people unscrambled sentences that contained suggestions of self control, they would immediately make better choices when it came to eating snacks.

Then we have mood memory which is where we recall memories which have the same emotional feeling as the way we feel at that moment.  So if we are sad, we are more likely to remember things that are sad.

Blanking out is something most of us have experienced at one time or another.  It has nothing to do with drinking but being so stressed out we forget things.  This usually happens during tests.  It turns out that if we are bored or too stressed, our performance is likely to suffer.  When we are bored, our minds are unfocused but if we are too stressed, our minds are too focused and we miss information.  The best place to be is when we are in moderate stimulation.

Finally, we have a duration memory because we do not remember everything involved with the memory.  Instead we remember the best or worst moment and the last moment.  We do not remember everything of the event.

This is why it is important to connect emotion with any learning, otherwise it won't stick.  In the future sometime, I'll cover emotions and learning math.  Let me know what you think, I'd love to hear.  Have a great day.

Chunking In A Digital Age

 With the way children's brains have been changing due to the use of digital devices, I wondered if chunking was still recommended or if it's been replaced by something else.

Chunking is one of the ways to organize information.  In reading, it is putting together letters and sounds to create meaning while in math it is organizing the information into smaller, more understandable pieces.

According to research, the human brain can only handle seven pieces of information in short-term memory at any one time.  Chunking the information helps the brain avoid traffic jams in short term memory.  Chunking also helps the brain remember more information because they have combined pieces together.

Chunking is also a way of identifying the most important information out of a section or chapter.  This is done so students know what they need to focus on and learn.  Furthermore, when chunked properly, it is well organized and logical and increases student information on what is going on.  It helps them see the bigger picture while remembering the information more effectively.

Furthermore, there is another theory, the cognitive loading theory, that states the more the brain has to remember in a shorter period of time, the more difficult it is to learn because the brain is overloaded.  This supports the use of chunking because chunking does not overload the brain. The chunking also allows them to build on previous chunks thus providing the repetition the brain needs to retain information.

It is known the brain seeks patterns to make sense of material because the brain stores information as patterns.  Furthermore, the information must make sense to the brain otherwise it will not be stored.  This includes new information that is not yet familiar so when we introduce new concepts, our brain does not always store it so we cannot expect our students to remember it after one example.  So it becomes necessary for teachers to help students identify the new patterns while associating them with older patterns in order to formulate new ones. Patterns have been described as the roadways for memories to travel.

In addition to looking for patterns, the brain searches for personal meaning so it is important to help students find a way to relate to the new patterns because that helps students learn the material better and easier.  If the brain cannot find personal meaning, it will lose it and we see it as students who don't "get it."  This often manifests as the "I don't care" attitude which students see as better than a "I don't understand" confession.

Since most of our students are used to working through quite a lot of data, we need to know how to organize multimedia materials into usable chunks.  It is recommended one group related information into each chunk.  This includes buttons, images, graphics, etc as related information.

There are some ways to help students find personal meaning.  One is to ask students to relate to the information in a personal way by writing it down on a KWL chart.  Another is to ask students to share a story with other students about something that happened to them that uses the concept you are teaching.  For instance, they might talk about when they ran out of gas because they didn't check the amount of gas in the tank before heading out.  This story might relate to a compound inequality about filling the tank with gas.

So with chunking and personal meaning, students can learn the material better and for longer periods of time.  let me know what you think, I'd love to hear.  Have a great day.