Attention

I'm sure we've all had the issue where we make sure every student has their eyes on the teacher before explaining something and then have a few students who ask "What are we supposed to do?".  It seems to happen every time.

Have you ever wondered about why they didn't hear you? We’ve  all heard that if you do not get people’s attention within the first few minutes minutes, you won’t get it.


 It turns out, it is a bit more complicated than that.  Yesterday, I listened to some TED radio show as I headed into town.  They interviewed a neuroscientist who has spent her whole life studying attention.  During the first part of the interview
she stated that most people would only hear about 4 out of 8 minutes of her talk.  In certain professions, hearing only 50 percent of what goes on could be detrimental such as a judge or perhaps a pilot.

According to Amishi Jha, we take our mind away from what is happening to let it wander.  We often allow our minds to travel back to events that have already happened.  We want to revisit them or we head to the future as we plan what we want to do.  We do this about 50 percent of the time because thoughts spontaneously pop in and our mind goes off.  This time wandering is one of two types of mind wandering. 

The other type is  often referred to as “daydreaming” where people all their mind to drift.  This type of mind wandering is what causes us to be creative.  This is also the type that occurs without missing other information.  Unfortunately, the down side is when our brains are occupied by other things, we have fewer chances for spontaneous thought to happen.

She said we are caught in this circle of when we experience external interruptions, we begin interrupting ourselves such as when we take a minute to check out the latest book by our favorite author or check our e-mails or texts.  These self imposed interruptions often become more and more frequent especially using mobile devices.  Many of our students stay up late checking out the latest text or responding before waiting for a reply.

Unfortunately, due to the exposure to more and more data, our brains do not have a chance to reboot.  Consequently, the term mindfulness has come into popularity in the last 20 years as the amount of data we subject our brains to has increased.  Mindfulness is where people take time away from life and meditate or enjoy some peace and quiet.  It gives our brains a chance to reboot and level out before we expose ourselves to the gigabytes of data.

So now you know why students often ask you "What am I supposed to do?"  Its because their minds wandered off.  Let me know what you think.  I'd love to hear.

Bingo

Every time I see suggestions for bingo, they are for use in the lower grades but I have been thinking of ways to use in my math classes.  So I am going to share some of the ideas I have come up with. Most of the possibilities require students to choose the answers from a list of possibilities. It is also expected, the list of possibilities will be two or three times the number of blank squares on a bingo card.

1. Common denominators - prepare a list of factors to produce a list of common denominators.  Have students write down several denominators on a blank bingo sheet.  Once students have filled out their cards, it is time to draw two numbers at a time. Students have to figure out the LCM and see if they have it.  See who gets the first Bingo.

2. Trinomials - prepare a list of factors which students choose two for each square. The teacher draws a trinomial for the students to factor. If they have the pair on their card, they can mark it off.

3. Dimensions for area or perimeter - students choose the measurements for a shape. The teacher draws the area or perimeter and students figure out the measurements. This could also be used for volume on certain shapes.

4. Words and equations - students choose from a list of equations and the teacher selects a verbal description and students see if they have it.

5. Algebraic fractions - provide a list of solutions for an assortment of problems. When ready start pulling problems out for students to solve. Once they find the answer, they see if they have it.

Other topics that would work in this same way include ratios, proportions, markups or mark downs, percent increase or decrease, nteger math, or just about any type of math you can imagine. It’s a matter of providing answers for their bingo cards.  It is just a matter of taking a little time to work things  out in preparation.

Let me know what you think, I would love to hear.

Writing Open Ended Questions

Ask students

We hear so much about integrating open ended questions in class but have you ever wondered
why?  What advantages are there to using open ended questions?  What is the best way to use them in class?

One great thing about open ended questions is there is not one correct answer.  Most textbooks are filled with problems designed to have only one possible solution. These problems are designed to be solved using a specific process.  Unfortunately, real life problems are not always as neatly solved as those in the textbooks.

In addition, these types of problems can be solved by students of different abilities with a differing level of knowledge.  These are perfect for differentiating the lessons to meet the needs of all students. These problems encourage student thinking and decision making. Textbook problems do not encourage students to develope their mathematical thinking.

The last thing these types of problems do is to help students develop their reasoning and communication abilities. The justification for the method chosen when working textbook problems is they use the method taught in the section. The reason for knowing the answer is it was in the back of the book.

The great thing about textbooks is they can provide problems which can be rewritten into open ended questions with a bit of adjustment.  First step is to start with the answer while throwing out the actual problem.  Instead of asking what 1/2 of 12 is, begin with the answer of 6.


Then create a question asking students to design a problem that gives produces that answer. So you could say 6 is a fraction of a number - what is that number and what is the fraction?

In addition there are a few other ways to create open ended questions for students.  One way is to ask students to compare and contrast numbers, shapes, graphs, probability, or measurements.  This requires more than something like 95 and 100 are different because one has 2 digits and the other has 3 digits.

Another way is to have students explain how something such as 5 is a factor of two numbers, what might be true for the two numbers? Or you could write a statement using soft words like almost or close such as two numbers multiplied together is almost 600?

Finally, have students make up sentences using numbers and mathematical words such as 8, 5, less, and. This allows for more than one answer.

If you have students who are not good at expressing their thoughts or using a more in depth explanation, these are some good ways to start students on their paths.  Let me know what you think, I would love to hear.

Happy Memorial Day

Warm-up

Warm-up

Data Mining in the Math Classroom.

  I've been hearing more and more about data mining.  I've decided it is time to look at what it is and how math is used because it is a real life application.   In many ways, it something to know more about as companies use data mining.

Data mining is simply the automated analysis of data looking for patterns and relationships among the data.  Sounds a lot like the definition of mathematics. 

Data mining uses aspects from linear algebra, multivariate statistics and optimization and the calculations can be quite sophisticated.   It is used in real life to find the best traffic route for the morning and evening traffic reports provided by both radio and television or places the tagging on our selfies, or prices of sale items or which movie to see.  We've all used the results of data mining.

This topic is important for students to be introduced to because  it is a prevalent part of our world.  There are a variety of lessons out there on data mining.  Texas CTE Resource Center has a nice introduction to the topic which requires students to do research to find the answers to several questions. 

The Kenan Fellows Program has a lesson on understanding data mining.  This one requires the school to download R statistical software to the servers along with the necessary data sets to analyze.  The lesson includes the lesson plan, student worksheets, and appropriate assessments.  This is geared more for AP statistics but could be done with any higher level math class.

We know that sites such as Facebook have gotten in trouble for using data mining but where does some of the data come from?  The site Teaching Privacy has a full lesson plan focused on your digital footprint and what information you leave with sites as you surf the internet. 

This lesson describes big data which is data that is too big to analyze by normal methods which in a sense describes data mining.  I love that it includes videos, questions, and a discussion of the exponential growth of data. 

Once students understand the basics of data mining, the University of Edinburgh offers data sets appropriate for students to practice data mining.  The sets include those the university deems as interesting and those that are not as good so students can look at both to determine which is better.  The data sets cover topics like particle physics, psychological data, brain-computer interface data, molecular bioactivity for drug design, etc.

So if you want to address the topic of data mining in your math class, this will give you the ability to teach it.  I am trying to figure out where I can integrate it in my lesson plans for next year. 

Let me know what you think, I'd love to hear.  Personally, I believe this is an important topic to introduce and it provides the basis of an authentic task using real world information and provides an opportunity for students to learn more about who uses data mining and for what.