Well, after 18 episodes of the Classroom Professor Math Podcast, I have decided to rationalize what I do to make more time for the most important parts of the business.
I have decided to continue to produce the video version of the podcast, but stop releasing audio versions. If you wish to subscribe, please go to iTunes and subscribe to the video podcast - just search for the podcast and select the video version. I will keep the existing audio recordings online for a while longer, as long as people appear to still find them useful.
If you'd like to let me know what you think, especially if you really like the audio recordings, email me at peter@classroomprofessor.com.
Sunday, September 4, 2011
Teach Math & Secure Communication
Another podcast in the series from our trip to the UK and Europe.
Royal Signals Museum
This time the podcast comes from the Royal Signals Museum in Blandford, Dorset, England. This museum is situated on an army base, so there is tight security to navigate before you can gain access to the museum. But the minor inconvenience is worth it, as the museum contains lots of displays that any teacher could make good use of with a upper primary/elementary or middle school class. As a bonus, at the security checkpoint we met a sergeant with a very dry wit who talked at length about his views on Margaret Thatcher, UK politics in general and the military that I found hilarious.Teach Math & Secret Codes
While travelling in the UK, I was thrilled to visit Bletchley Park, Milton Keynes, UK. This little town, around 45 minutes north of London, is not that well known, but was the centre of a major war effort during WWII.
The technology developed at Bletchley Park by Alan Turing, Tommy Flowers and a huge team of workers has echoes even today, in electronic programmable computers and secure encryption and decryption of messages.
The technology developed at Bletchley Park by Alan Turing, Tommy Flowers and a huge team of workers has echoes even today, in electronic programmable computers and secure encryption and decryption of messages.
Teach Roman Math
Teach your students about Roman civilization with a math connection!
I visited Chester in North England, where my brother lives with his family (he appears briefly in the video with his wife, and my wife and I). Chester is a fascinating town, which stands on top of Roman ruins, many of which no doubt have not yet been found. Basically, whenever a new building project gets underway, archaeologists have to be called in if (or more likely when) ruins are found on the site.
I visited Chester in North England, where my brother lives with his family (he appears briefly in the video with his wife, and my wife and I). Chester is a fascinating town, which stands on top of Roman ruins, many of which no doubt have not yet been found. Basically, whenever a new building project gets underway, archaeologists have to be called in if (or more likely when) ruins are found on the site.
Connect Science & Technology in Math Lessons
My wife and I visited family in in England, Scotland and South Wales, and so had opportunities to visit various sites near where family members live. Two of these locations are featured in this week’s podcast.
Outside there is a Keep (small tower) on top of a steep mound, called a “motte”, which the energetic can climb up, including climbing some really steep stairs to the top of the keep.
Now, in the grounds of the castle is a working trebuchet, which apparently was constructed for use in the 2011 movie Ironclad (click to see trailers – including shots of the trebuchets). The castle asked if they could have it when the movie was finished, and there it is. The machine is “fired” (is that what you call it?) periodically for the public. We missed seeing it shot by one day – what a shame. Still, I got to stand in front of it uninterrupted to talk about science, technology and math.
Stonehenge
First, Stonehenge, in Wiltshire. This site was built in pre-historic times, meaning that its precise origins were not recorded in writing and so working out why it is there, how it was constructed and what it meant at the time can only be deduced by experts in archaeology and history.Cardiff Castle
Later in our trip, we had a trip to Cardiff, and a local historical site, Cardiff Castle. I can thoroughly recommend it as a fun day out for families or couples. The main castle building itself has some beautifully furnished rooms, and, for royal watchers, some nice connections with the Royal Family.Outside there is a Keep (small tower) on top of a steep mound, called a “motte”, which the energetic can climb up, including climbing some really steep stairs to the top of the keep.
Now, in the grounds of the castle is a working trebuchet, which apparently was constructed for use in the 2011 movie Ironclad (click to see trailers – including shots of the trebuchets). The castle asked if they could have it when the movie was finished, and there it is. The machine is “fired” (is that what you call it?) periodically for the public. We missed seeing it shot by one day – what a shame. Still, I got to stand in front of it uninterrupted to talk about science, technology and math.
Teaching Slope in the Mountains of Switzerland
Switzerland is known for its beautiful mountains and chocolate-box scenery, summer or winter. My wife and I were blessed to visit there this last spring, so I took the opportunity to video another podcast episode. We took a cable car up a smallish mountain near Lucerne; actually probably just a hill by Swiss standards, then walked down. We'd done this before on a higher mountains when we were younger and fitter, and ended up unable to walk the next day. So this time we were a bit wary of taking on too much.
So, what about the math in this setting? The cable car and the incredible mountains, and the road tunnels that go through them all got me thinking. The swiss have developed an impressive network of roads that enable a driver to travel all over the country, in spite of the mountains that threaten to prevent travel due to their sheer size and their steep slopes.
To cater for this steep topology, Swiss engineers have put in place cable cars, modified railways, tunnels and myriad other installations to respond to the terrain. Sloped paths, steps, zig-zag roads and a thousand other examples allow life to happen in among the mountains.
So, what about the math in this setting? The cable car and the incredible mountains, and the road tunnels that go through them all got me thinking. The swiss have developed an impressive network of roads that enable a driver to travel all over the country, in spite of the mountains that threaten to prevent travel due to their sheer size and their steep slopes.
To cater for this steep topology, Swiss engineers have put in place cable cars, modified railways, tunnels and myriad other installations to respond to the terrain. Sloped paths, steps, zig-zag roads and a thousand other examples allow life to happen in among the mountains.
What is REALLY Important in Teaching Math?
You are a math teacher. You know what works, what doesn't and what frustrates you about your work in your classroom.
In this podcast episode, I chat with you about what is really important in the teaching of math. At the end of the video, I ask you a question and a favor. Please respond.
In this podcast episode, I chat with you about what is really important in the teaching of math. At the end of the video, I ask you a question and a favor. Please respond.
Teaching Symmetry in Paris
This podcast follows last week's (Episode 11), and discusses further locations in Paris and France, including L'Arc de Triomphe and Le Château de Versailles (The Palace of Versailles).
To gain a full perspective on this episode, go to the video version. The video is in three short sections, starting with a classroom revision of symmetry and its two forms, then on location at l'Arc de Triomphe. Lastly is a sequence of shots from the locations listed above, put to music. The mp3 version omits the third section, since the audio track is just music.
To gain a full perspective on this episode, go to the video version. The video is in three short sections, starting with a classroom revision of symmetry and its two forms, then on location at l'Arc de Triomphe. Lastly is a sequence of shots from the locations listed above, put to music. The mp3 version omits the third section, since the audio track is just music.
Use Public Spaces to Teach Symmetry
My wife and I recently were blessed to visit Paris, and spent an afternoon at La Grande Arche, Paris, which houses government offices.
I videoed a short clip about using public buildings in any city to teach symmetry and other math topics. La Grande Arche (in French, 'The Big Arch') exhibits both reflectional, or mirror, symmetry and rotational, or point, symmetry. Lots of other public buildings offer similar opportunities for investigating this sort of math topic.
I videoed a short clip about using public buildings in any city to teach symmetry and other math topics. La Grande Arche (in French, 'The Big Arch') exhibits both reflectional, or mirror, symmetry and rotational, or point, symmetry. Lots of other public buildings offer similar opportunities for investigating this sort of math topic.
Math and Canal Technology
This recording for math teachers was made on location, at a set of locks in Chester, England.
Locks are an example of amazingly ingenious technology, invented hundreds of years ago and still working today. Without any electricity, fossil fuels or other 'external' sources of energy, locks merely use the power of gravity as it acts on water in an enclosed lock. The water flows into a closed section of the canal, causing the barge in that section to rise, and so raises a boat from a lower section of the canal to a higher one, in a few minutes.
Locks are an example of amazingly ingenious technology, invented hundreds of years ago and still working today. Without any electricity, fossil fuels or other 'external' sources of energy, locks merely use the power of gravity as it acts on water in an enclosed lock. The water flows into a closed section of the canal, causing the barge in that section to rise, and so raises a boat from a lower section of the canal to a higher one, in a few minutes.
Teach Measuring Time
This recording was made on location at Le Musée d'Histoire des Sciences (Museum of the History of Science), Geneva, Switzerland. The museum has some rather cool exhibits outside (in bright sunshine the day we were there), showing different sorts of sundials.
Teaching time is a really important topic in mathematics, both in terms of time of day and duration of events. There are neat connections to make between math and technology of measuring time, giving lots of material to the creative teacher.
Teaching time is a really important topic in mathematics, both in terms of time of day and duration of events. There are neat connections to make between math and technology of measuring time, giving lots of material to the creative teacher.
Advanced Number Facts Strategies
How should we teach the advanced Number Facts?
See the previous episode of the podcast for the first five strategies for teaching multiplication number facts. This episode deals with the more difficult facts, up to 12x12. If the recommended sequence is followed, as students progress through the facts, they have fewer and fewer to learn, since many will have been covered in previous sets. For example, when learning the 6x number facts in this system, students have already learned these facts, and so only have to revise them:- 2x6
- 10x6
- 5x6
- 3x6
- 4x6
- 0x6
- 11x6
- 6x6
The Best Number Facts Strategies
What are the best ways to teach Number Facts?
Students need a way to help them remember their multiplication number facts. Teachers need a way to teach these facts without it taking all day to do it. The curriculum isn't what it was in 1911; in 2011 we have to fit an aweful lot more into the day. Students' expectations aren't the same either; they expect to be able to use the latest technology in their leisure activities and in their learning, and want to know that what they learn in class is going to be useful.Number Facts Strategies to the rescue! The recommended strategies in the next two podcast episodes will assist the busy teacher to systematically teach multiplication number facts in a way that makes sense to students, by helping them to concentrate on characteristics of the numbers they are learning about.
Practical Math - Number Facts
'Ordinary folks' - those who are not teachers - sometimes criticize teachers for being too concerned about educational theory and not enough about the practical needs of students, their families and future workmates.
The challenge is, of course, that as a profession, education is an academic discipline which is founded on centuries of careful research and writing by our professional predecessors. It would be wrong, and quite foolish, to ignore the foundations laid at the beginning of general public education, and the myriad advances in understanding of learning and teaching that have taken place since then.
Nevertheless, people outside academic institutions often have quite clear expectations of teachers' work, and expect us to prepare our students to take their places as functional, productive members of society.
In this podcast Peter Price argues that number fact memorization is essential for all students.
The challenge is, of course, that as a profession, education is an academic discipline which is founded on centuries of careful research and writing by our professional predecessors. It would be wrong, and quite foolish, to ignore the foundations laid at the beginning of general public education, and the myriad advances in understanding of learning and teaching that have taken place since then.
Nevertheless, people outside academic institutions often have quite clear expectations of teachers' work, and expect us to prepare our students to take their places as functional, productive members of society.
Number Fact Memorization
Number facts need to be memorized if one is to have any chance at using math for anything really useful, both in the classroom and in the outside world. This is one example in which setting a priority will fulfill aspirations in both contexts; students will need to recall number facts in lots of (all?) future math classes, and in "real life" also.In this podcast Peter Price argues that number fact memorization is essential for all students.
Teach Metric Units: The Cubic Meter
Most nations of the world (all except Myanmar - Burma, Liberia and the United States of America) use the metric system of measurement units (officially: SI Units).
The first half of this podcast is spent discussing the article Metrication in the United States (Wikipedia), which highlights the history of metrication in the US since 1866 until today.
In the second half, Peter Price describes a useful Cubic Meter Kit, to teach students the meaning of this unit and its size.
The first half of this podcast is spent discussing the article Metrication in the United States (Wikipedia), which highlights the history of metrication in the US since 1866 until today.
In the second half, Peter Price describes a useful Cubic Meter Kit, to teach students the meaning of this unit and its size.
Show ANY Number With Number Lines
Number lines are another versatile resource for classroom math teachers. Since numbers are both abstract entities with no physical existence and infinite in extent, helping students to understand them is essential if they are to make sense of the math they learn in school. Thankfully, unlike resources such as place value blocks or counters, number lines are capable of representing any finite number.
In this podcast, a basic discussion of number lines and their usefulness is supplemented by examples for each of the basic operations. The video version of the podcast includes graphics to illustrate each example.
One significant benefit from using number lines is the flexible ways they can be used, helping students to develop their skill in mentally picturing quantities and operations on them. Don't try to force students to use number lines in a rigid, teacher-directed way, but ask students to come up with their own representations.
In this podcast, a basic discussion of number lines and their usefulness is supplemented by examples for each of the basic operations. The video version of the podcast includes graphics to illustrate each example.
One significant benefit from using number lines is the flexible ways they can be used, helping students to develop their skill in mentally picturing quantities and operations on them. Don't try to force students to use number lines in a rigid, teacher-directed way, but ask students to come up with their own representations.
Quit Moving the Decimal Point!
Place value slides are a fantastic resource to teach what happens when numbers are multiplied or divided by a power of 10 (10, 100, 1000 or 0.1, 0.01, 0.001, etc.). The "traditional" method of teaching students to "move the decimal point" is crap, and should NEVER be taught. But to listen to lots of young adults (such as many of my preservice teacher students), that is exactly what they have been told. And unless they understand what I teach in this video, that's what their students will learn.
Decimal points do not move. Ever. Even in a bad math lesson. The decimal point exists to separate ones from tenths, or whole number places from decimal fraction places. Telling students to move the decimal point is like asking them to rearrange the letters of the alphabet because it happens to suit the teacher's strange ideas of alphabetical order.
Use a place value slide to demonstrate the "shifting" of every digit left or right as a number is multiplied or divided by a power of ten. Making a place value slide involves use of a sharp knife, and so should be done by an adult. But the effort is worth it in demonstrating clearly what happens within the base ten system when multiplying by a power of ten, such as when converting metric measurements or calculating with percentages.
Decimal points do not move. Ever. Even in a bad math lesson. The decimal point exists to separate ones from tenths, or whole number places from decimal fraction places. Telling students to move the decimal point is like asking them to rearrange the letters of the alphabet because it happens to suit the teacher's strange ideas of alphabetical order.
Use a place value slide to demonstrate the "shifting" of every digit left or right as a number is multiplied or divided by a power of ten. Making a place value slide involves use of a sharp knife, and so should be done by an adult. But the effort is worth it in demonstrating clearly what happens within the base ten system when multiplying by a power of ten, such as when converting metric measurements or calculating with percentages.
Teach 1-20 With Ten Frames
Ten frames are possibly the most useful resource a teacher can use to help students understand numbers to 20, including addition and subtraction facts for these numbers. In this episode I explain how ten frames can be used in this way.
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