I was in a global math department "hangout" the other day. One of the teachers presenting provided a great professional development opportunity for teachers to take to their teams and get feedback from students on how their lesson went.

The professional development looks like this:

go to a charity shop, find a game, design a lesson around it.

The teacher who presented found a game at a charity shop that was Marble Run. A marble takes turns round and round and the students had to find the plot the graph for distance vs. time. This is a great graphing stories, an extension of this activity is having students create posters with the plots.

This shows that any teacher can go out and design a lesson around a game they find for cheap. I have found many other teachers using these same ideas for using games around the classroom.

What games do you use in the classroom? Do you think you could use a game around a lesson next week? Could you do this with the faculty you work with?

Check out global math department videos here: https://www.bigmarker.com/GlobalMathDept

### Forgetting Proofs

I was reading Naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity by Loren R. Graham and I came across a great little quote, but we will get back to that later. The book was like Paul Erdos book The Man Who Loved Only Numbers style of quick writing. It was a fascinating book with history of some of the most famous Russian mathematicians of the 19th- 20th Century. This book reminded me of a professor that I had at the University of Nebraska at Omaha.

My rating: 4 of 5 stars

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A quick quote gave me inspiration to get students up to the board.

He would begin a proof at the blackboard, pause, and then say, "I cannot recall the proof; perhaps one of my colleagues could remind me." This was a challenge that the class felt obligated to meet. One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face. Another would get up, perhaps a 17 year old, successfully write the proof on the blackboard while the entire class stared enviously, and then sit down. Professor Luzin would turn to that student, bow slightly, and say "Thank you, my colleague." Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures.

One of them later ask, "Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence?" They never knew.

This small process of accidentally forgetting the proof or answer to an example is a great way to get students up to the board and motivated to do mathematics. I especially love the part where the instructor bows to the student and offers a sincere Thank you and recognizes the student as an equal, in mathematics you are always trying to get students to enjoy math and approve of their mathematics.

How could you incorporate this small idea of forgetting proofs in to your teaching? What benefit do you think would this have in your classroom? How do you do this now in your room?

My rating: 4 of 5 stars

View all my reviews

A quick quote gave me inspiration to get students up to the board.

He would begin a proof at the blackboard, pause, and then say, "I cannot recall the proof; perhaps one of my colleagues could remind me." This was a challenge that the class felt obligated to meet. One student would jump up, go to the blackboard, attempt the proof, fail, and then sit down with a red face. Another would get up, perhaps a 17 year old, successfully write the proof on the blackboard while the entire class stared enviously, and then sit down. Professor Luzin would turn to that student, bow slightly, and say "Thank you, my colleague." Luzin treated the students as intellectual equals, and his teaching led them to prepare for and anticipate coming lectures.

One of them later ask, "Had Luzin [really] forgotten the proof, or was it a well-constructed game, a method of arousing activity and independence?" They never knew.

This small process of accidentally forgetting the proof or answer to an example is a great way to get students up to the board and motivated to do mathematics. I especially love the part where the instructor bows to the student and offers a sincere Thank you and recognizes the student as an equal, in mathematics you are always trying to get students to enjoy math and approve of their mathematics.

How could you incorporate this small idea of forgetting proofs in to your teaching? What benefit do you think would this have in your classroom? How do you do this now in your room?

### Using Instagram in Math Class

Instagram is a free, fun, and simple way to make and share photos on the iPhone and iPad. Students pick from one of several filtered effects to breathe new life into mobile photos. Students can transform everyday moments in the classroom in see and to works of art. Students can show photos in a simple photo stream with friends, classmates, teachers, and family.

There are some examples below where you can use Instagram in the classroom:

Turn a dry subject with numbers and formulas, and connect it to art through visual expression. Younger students can capture mathematical concepts through visual problem solving re-enactments (like word problems) or even snapping photos of complex formulas designed on poster board.

Every month, take a few photos of the student’s progress. Families can follow the classroom account and keep up with what their child is learning and doing.

Parents and community members love to know about the teachers who work in the schools. Have the kids interview all the teachers in a school, writing up a bio of each instructor and tagging a photo of them on Instagram. The filters make even the poorest photos look professional! You can take pictures of homework questions or even some of the answers to the problems.

Similar to digital storytelling, this would allow students to explore issues in their world through a visual medium. I want them to engage in citizen journalism. Students can use the mobile devices to express their social voice and find math in the real world by tying together photos of math concepts and definitions.

Last year, I found photographs and created writing prompts. Sometimes, they were geared toward poetry or narrative while other times they were persuasive or informational. I will encourage students to develop their own photo prompts using Instagram. Having photos where students come up with their own math story problems by a photo.

I will give students concepts from any of the subject areas and ask students to find a metaphor that fits the concept. They will use Instagram to find the metaphor and then describe it in the comments section.

What ways can you think of where you could use Instagram in your classroom? What other types of iPad applications do you use in the math classroom?

Check out two sites that offer educational ways of incorporating Instagram into the classroom below:

10 Instagram Ideas

Creative Ways of using Instagram

Download the app here: Instagram

There are some examples below where you can use Instagram in the classroom:

__Problem Solving__Turn a dry subject with numbers and formulas, and connect it to art through visual expression. Younger students can capture mathematical concepts through visual problem solving re-enactments (like word problems) or even snapping photos of complex formulas designed on poster board.

__Classroom Account__Every month, take a few photos of the student’s progress. Families can follow the classroom account and keep up with what their child is learning and doing.

__Teacher Photos__Parents and community members love to know about the teachers who work in the schools. Have the kids interview all the teachers in a school, writing up a bio of each instructor and tagging a photo of them on Instagram. The filters make even the poorest photos look professional! You can take pictures of homework questions or even some of the answers to the problems.

__Math in the Real World__Similar to digital storytelling, this would allow students to explore issues in their world through a visual medium. I want them to engage in citizen journalism. Students can use the mobile devices to express their social voice and find math in the real world by tying together photos of math concepts and definitions.

__Math Prompts__Last year, I found photographs and created writing prompts. Sometimes, they were geared toward poetry or narrative while other times they were persuasive or informational. I will encourage students to develop their own photo prompts using Instagram. Having photos where students come up with their own math story problems by a photo.

__Metaphors in Math__I will give students concepts from any of the subject areas and ask students to find a metaphor that fits the concept. They will use Instagram to find the metaphor and then describe it in the comments section.

What ways can you think of where you could use Instagram in your classroom? What other types of iPad applications do you use in the math classroom?

Check out two sites that offer educational ways of incorporating Instagram into the classroom below:

10 Instagram Ideas

Creative Ways of using Instagram

Download the app here: Instagram

### KUCE Taxonomy

I was trying to think of ways of implementing more Bloom's Taxonomy in my classroom and I had an epiphany. Bloom's Taxonomy is dated for 21st Century learners and does not give students the freedoms of a classroom atmosphere for the real-world. So I came up with my own taxonomy: KUCE Taxonomy. It takes bits and pieces from Bloom's along with some adaptations of my own.

In Bloom's Taxonomy the first two base stages of the pyramid are remember and understand and if you combine these two bases together you get know. Students remembering and understanding the material is normally done in one or two days depending on the material. Students in most classrooms listen to lectures and either understand or don't. In my classroom I want students to know the material and be able to get to the next step in the learning process as quickly as possible. I believe that knowing something is just the first step in the process of learning.

Again in Bloom's Taxonomy the next two steps in the pyramid are Apply and Analyze, in my understanding this is using the material that you know. After students know and understand the material, I want them to use the material in my classroom, in the picture below of the actual taxonomy it is semi-broken down into two different parts: examples and real world. I put a wavy line between the two, because you can use different ways of using the material and sometimes it may not be examples or going as far to the real world, but the line is blurred and in my classroom I want to have students come up with examples and once they have mastered using examples I want them to learn how to use this information in the real-world.

Once students know the material and can use the material, the next logical step is create and in Bloom's Taxonomy this changes a little bit (Bloom has it at the pinnacle of the pyramid). Once again I have semi-broken down the creative stage in to two parts: local/community and global. For 21st Century learners, students need to be able to apply their knowledge in their community and globally, students need to be informed citizens and care about the world they live in. The arrows are in their, because students need to be moving in the direction of global learning and thinking about others outside of their local bubbles. In my classroom for example, students might create a presentation for the classroom then students set up either a website to take their use of knowledge to the next level the global web. In other classrooms it might be researching tyrannies in other parts of the world, not just their own backyard.

At this point, in my classroom, students have mastered the material. They have become small masters of the material and once they have completed something on the global scale they can evaluate others work. This might be in the sense that they can evaluate a math website for mistakes or in other classrooms students are able to evaluate other governments for flaws and successes other than their own. Students become well-rounded and are able to make decisions on their own from the previous sections of knowledge. They know the material, use it, created their own projects, and are now prepared for the real world.

Now that you have most of the information the KUCE Taxonomy is built for life-long learners in a pluralistic society, students are well-rounded and prepared for anything. This system of learning in schools is not adopted yet, but I hope to think that master teachers and reformists in education are built towards this style of learning. I believe that children are built for learning new things, just not in the classroom but on their own.

The last thing I want to include is the shape I built in for the taxonomy. The trapezoid shape is developed not only for time students should be spending on each stage, but learning increases as you go up the ladder. In Bloom's Taxonomy it is a pyramid with a point top, for me this is where learning stops. In the KUCE Taxonomy it has a open top, learning never stops. As teachers, we know this all too well.

If you have any comments or suggestions about changes to the taxonomy, please post them below. How do you think learning would change with these steps instead of Bloom's? How do you think you could shape your curriculum to fit these stages?

__K: Know__In Bloom's Taxonomy the first two base stages of the pyramid are remember and understand and if you combine these two bases together you get know. Students remembering and understanding the material is normally done in one or two days depending on the material. Students in most classrooms listen to lectures and either understand or don't. In my classroom I want students to know the material and be able to get to the next step in the learning process as quickly as possible. I believe that knowing something is just the first step in the process of learning.

__U: Use__Again in Bloom's Taxonomy the next two steps in the pyramid are Apply and Analyze, in my understanding this is using the material that you know. After students know and understand the material, I want them to use the material in my classroom, in the picture below of the actual taxonomy it is semi-broken down into two different parts: examples and real world. I put a wavy line between the two, because you can use different ways of using the material and sometimes it may not be examples or going as far to the real world, but the line is blurred and in my classroom I want to have students come up with examples and once they have mastered using examples I want them to learn how to use this information in the real-world.

__C: Create__Once students know the material and can use the material, the next logical step is create and in Bloom's Taxonomy this changes a little bit (Bloom has it at the pinnacle of the pyramid). Once again I have semi-broken down the creative stage in to two parts: local/community and global. For 21st Century learners, students need to be able to apply their knowledge in their community and globally, students need to be informed citizens and care about the world they live in. The arrows are in their, because students need to be moving in the direction of global learning and thinking about others outside of their local bubbles. In my classroom for example, students might create a presentation for the classroom then students set up either a website to take their use of knowledge to the next level the global web. In other classrooms it might be researching tyrannies in other parts of the world, not just their own backyard.

__E: Evaluate__At this point, in my classroom, students have mastered the material. They have become small masters of the material and once they have completed something on the global scale they can evaluate others work. This might be in the sense that they can evaluate a math website for mistakes or in other classrooms students are able to evaluate other governments for flaws and successes other than their own. Students become well-rounded and are able to make decisions on their own from the previous sections of knowledge. They know the material, use it, created their own projects, and are now prepared for the real world.

Now that you have most of the information the KUCE Taxonomy is built for life-long learners in a pluralistic society, students are well-rounded and prepared for anything. This system of learning in schools is not adopted yet, but I hope to think that master teachers and reformists in education are built towards this style of learning. I believe that children are built for learning new things, just not in the classroom but on their own.

The last thing I want to include is the shape I built in for the taxonomy. The trapezoid shape is developed not only for time students should be spending on each stage, but learning increases as you go up the ladder. In Bloom's Taxonomy it is a pyramid with a point top, for me this is where learning stops. In the KUCE Taxonomy it has a open top, learning never stops. As teachers, we know this all too well.

If you have any comments or suggestions about changes to the taxonomy, please post them below. How do you think learning would change with these steps instead of Bloom's? How do you think you could shape your curriculum to fit these stages?

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### Calculating Weather Probability

When multiplying decimals or percentages in your classroom a great way to incorporate real-world scenarios is how weatherman get their predictions of a percentage of rain in your area. Take for example the 7 day forecast located to the right.

There is a 30% chance of rain on Saturday, how did they come up with that percentage.

Forecasts issued by the National Weather Service routinely include a "PoP" (probability of precipitation) statement, which is often expressed as the "chance of rain" or "chance of precipitation".

ZONE FORECASTS FOR NORTH AND CENTRAL GEORGIA NATIONAL WEATHER SERVICE PEACHTREE CITY GA 119 PM EDT THU MAY 8 2008

GAZ021-022-032034-044046-055-057-090815-CHEROKEE-CLAYTON-COBB-DEKALB-FORSYTH-GWINNETT-HENRY-NORTH FULTON-ROCKDALE-SOUTH FULTON-INCLUDING THE CITIES OF...ATLANTA...CONYERS...DECATUR...

EAST POINT...LAWRENCEVILLE...MARIETTA 119 PM EDT THU MAY x 2008

.THIS AFTERNOON...MOSTLY CLOUDY WITH A 40 PERCENT CHANCE OF SHOWERS AND THUNDERSTORMS. WINDY. HIGHS IN THE LOWER 80S. NEAR STEADY TEMPERATURE IN THE LOWER 80S. SOUTH WINDS 15 TO 25 MPH. .TONIGHT...MOSTLY CLOUDY WITH A CHANCE OF SHOWERS AND THUNDERSTORMS IN THE EVENING...THEN A SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS AFTER MIDNIGHT. LOWS IN THE MID 60S. SOUTHWEST WINDS 5 TO 15 MPH. CHANCE OF RAIN 40 PERCENT.

There is a 30% chance of rain on Saturday, how did they come up with that percentage.

Forecasts issued by the National Weather Service routinely include a "PoP" (probability of precipitation) statement, which is often expressed as the "chance of rain" or "chance of precipitation".

__An____example of this__:ZONE FORECASTS FOR NORTH AND CENTRAL GEORGIA NATIONAL WEATHER SERVICE PEACHTREE CITY GA 119 PM EDT THU MAY 8 2008

GAZ021-022-032034-044046-055-057-090815-CHEROKEE-CLAYTON-COBB-DEKALB-FORSYTH-GWINNETT-HENRY-NORTH FULTON-ROCKDALE-SOUTH FULTON-INCLUDING THE CITIES OF...ATLANTA...CONYERS...DECATUR...

EAST POINT...LAWRENCEVILLE...MARIETTA 119 PM EDT THU MAY x 2008

.THIS AFTERNOON...MOSTLY CLOUDY WITH A 40 PERCENT CHANCE OF SHOWERS AND THUNDERSTORMS. WINDY. HIGHS IN THE LOWER 80S. NEAR STEADY TEMPERATURE IN THE LOWER 80S. SOUTH WINDS 15 TO 25 MPH. .TONIGHT...MOSTLY CLOUDY WITH A CHANCE OF SHOWERS AND THUNDERSTORMS IN THE EVENING...THEN A SLIGHT CHANCE OF SHOWERS AND THUNDERSTORMS AFTER MIDNIGHT. LOWS IN THE MID 60S. SOUTHWEST WINDS 5 TO 15 MPH. CHANCE OF RAIN 40 PERCENT.

What does this "40 percent" mean? ...will it rain 40 percent of of the time? ...will it rain over 40 percent of the area?

The "Probability of Precipitation" (PoP) describes the chance of precipitation occurring at

*point you select in the area.***any**
How do forecasters arrive at this value?

Mathematically, PoP is defined as follows:

PoP = C x A where "C" = the confidence that precipitation will occur

*in the forecast area, and where "A" = the percent of the area that will receive measureable precipitation,***somewhere****if it occurs at all.**
So... in the case of the forecast above, if the forecaster knows precipitation is sure to occur ( confidence is 100% ), he/she is expressing how much of the area will receive measurable rain. ( PoP = "C" x "A" or "1" times ".4" which equals .4 or 40%.)

*But*, most of the time, the forecaster is expressing a combination of degree of confidence

*and*areal coverage. If the forecaster is only 50% sure that precipitation will occur, and expects that,

*if it does occur,*it will produce measurable rain over about 80 percent of the area, the PoP (chance of rain) is 40%. ( PoP = .5 x .8 which equals .4 or 40%. )

In either event, the correct way to interpret the forecast is: there is a 40 percent chance that rain will occur at any given point in the area.

Explaining "Probability of Precipitation": http://www.srh.noaa.gov/ffc/?n=pop

You can have your students multiple percentages and come up with their own weather forecast for the surrounding area for the next couple of days and see if the weatherman in your area are more accurate at predicting than you are.

Do you think you could put more real-world scenarios in your classroom? Is this a good example to start with in your room?

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