Flipping the classroom

I am currently playing with the idea of flipping my classroom.

What is that? It is a new way to think of how to use working time in class versus working time at home.

In a traditional setting, class time is largely spent with the teacher doing most of the talking and possibly students doing some independent work at the end of the period. Then homework is generally students trying to work independently at home on some sort of practice.

With "flipping" these roles are reversed. At home students watch short videos of the teacher teaching concepts that otherwise would have been taught during class time. During class time students practice the skill that was taught in the previous night's video(s).

My initial plan for "flipping":

• Each evening at home students watch a short video of me teaching a concept. They take notes on my video, pausing and replaying as needed. They may even do a problem or two just to make sure they understand the concept. 
• At school the next day, students then self-select one of three groups: 1.) students who absolutely understood the previous night's video and are ready to move on to some sort of enrichment; 2.) students who somewhat understood the concept and want to work collaboratively with other students to further develop proficiency with the concept; and 3.) students who are totally confused and need additional direct instruction from me.

What are the PROs and CONs of such a system?

PROs:

1. True differentiation can occur during note-taking. During "lecture" time at home, students can pause, rewind, and replay as often as needed while taking notes. No more are ALL students subjected to the same lecture experience.
2. True differentiation can occur during class time. Since students are no longer spending 85% of their class time taking notes, they can use that time to actually practice the concepts they are supposed to be learning. However, the added benefit is that students can pick the level of involvement that best meets their need at that particular time: enrichment, working with peers on practice problems, or receiving additional direct instruction.
3. Students who are absent can still view my lectures online, which reduces the amount they fall behind while absent.
4. Flipping more closely mirrors how learning actually happens outside school. If the Internet and YouTube and Google exist, why are classrooms still behaving as if the teacher is the only purveyor of all knowledge?

CONs:

1. Equity issues. What about those students who do not have access to the Internet at home?
2. Motivational issues. Students are loathe to do homework. Will watching videos as "homework" increase motivation or decrease motivation? Are students motivated enough to do the "learning" at home while doing the "practice" in the classroom?
3. Making the videos is time consuming and requires significant advanced planning.

My initial responses to each of the CONs:
#1: Sure equity is an issue...it is already an issue with the status quo of traditional teaching, however. What is so equitable about subjecting all students to the exact same lecture in a traditional classroom? In a traditional class period, the top students are bored with the lecture while the bottom students are completely lost. Perhaps only the middle students are actually benefitting from the lecture. While flipping a classroom might create one equity issue (access to Internet), it solves a greater equity issue (access to appropriate instructional experience).

#2: I suspect students will be more motivated to watch short lecture videos rather than doing a bunch of problems from a textbook. Some studies have shown that videos on demand improve student learning in mathematics, science, and social studies.

#3: This is true, however, one does not have to make all one's own videos. There are thousands of videos already created on the Internet. One merely needs to find them in advance and provide the links for the students at home.

I am sure there are plenty of things (PROs and CONs) that I have not mentioned. What are some?

Empty Number Line 2

Empty Number Line

Here is a great resource for seeing the empty number line in action with adding and subtracting whole numbers.

Empty number line

When I teach new mathematical concepts to my students, I always try to use some sort of visual model to make the learning easier. No duh! But what I have noticed is that over the years I have collected an odd assortment of models to teach everything without any theme to all the models. The model for teaching fractions looks nothing like the model for integers.

By the end of the school year, the models I intended to make learning mathematics easier began to get jumbled in the minds of my students. No good.

Recently I found the empty number line, which I hope to use as a unifying model that can work in a variety of different math concepts.

The empty number line is simply a line without regular intervals and without the zero being indicated unless needed. Students can use the number line to record their thoughts for solving the problem. Below are small examples of how the empty number line can be used in various math concepts:

Using the empty number line to add whole numbers:

Starting on the empty number line at 347, we make a series of hops that have a sum of 285. Where we end up on the number line is the solution to 347 + 285.

Using the empty number line to subtract whole numbers:

To model subtraction, you begin by placing 386 and 512 on the empty number line. Then using any series of hops, find the distance from 386 to 512. In the example above, 4 is added to get to 390. Then 10 is added to get to 400. Then 100 is added to get to 500. Finally, 12 is added to get to 512.

Summing the hops from 386 to 512 gives us the difference of 512 and 386.

4 + 10 + 100 + 12 = 126

The REAL power of using the empty number line is that it builds number sense in the students. It causes the focus to shift from the students trying to memorize an algorithm to students developing number sense while making up their own series of hops along the number line.

This becomes very apparent with subtracting fractions.

Using the empty number line to subtract a mixed number from a whole:

Example 1

To subtract, we need to think of finding the distance between the two numbers. In the above example, we place $5\frac{2}{9}$ and 18 on the number line and then use any series of hops to find the distance from one to the other. The drawn number line shows a hop of $\frac{7}{9}$ and a hop of 12. This means the difference is $12\frac{7}{9}$.

Example 2

Using the empty number line to subtract mixed numbers with the same denominator:

Example 1

After placing $5\frac{8}{9}$ and $13\frac{7}{9}$, we can use three hops to find that the distance is $7\frac{8}{9}$.

Example 2

Using the empty number line to subtract mixed numbers with different denominators:

Example 1

In this example we can use three hops to find the distance from $2\frac{2}{3}$ to $6\frac{1}{4}$. However, we need to get a common denominator to find that the difference is $3\frac{7}{12}$.

If you have any questions or comments on using the empty number line, please speak up!