Mimetic Lesson #1: {Math} Value, Place Value, & Simple Value

Have no idea what Socratic and mimetic instruction are?  Visit the Classical Modes of Teaching Main page to find out– before you listen to this lesson. Make sure to print out the Classical Teaching Study Sheets before you begin the lesson. (The study sheets aid in your learning and help you know what to listen for.)

[box] Thank you for seeking to learn more about the classical modes of teaching. I am grateful you are taking the time to do so. I too am learning more each time I teach. It is a bit scary to begin sharing all these lessons, but I know this is an area we all desperately need to need to learn about grow in, so I am doing it anyway. The lessons I upload and the assessments I give each lesson are in no way the end all be all of classical teaching. They are however steps along the path and my way of helping a fellow classical educators dive deeper into this tradition. I pray this space becomes a place where we all can learn from each other as co-inquirers into the truth. Thank you for being a part of this community.[/box]

Here is Mimetic Lesson #1.

{Warning: we are kind of silly and my laugh is kind of  loud, and there were a few distractions. I tried to keep as much of the recording as I could so you can see this is possible in real life with real kids and all that it brings.}

My Assessment of the Lesson

LOGOS: You can think about the value of a number according to its local/place value, its value, and its simple value.

TEXT: Ray’s Practical Arithmetic

Invitation

{what was done well}

Since our lesson was mostly about place value, showing Josiah that he already knew somethings about place value was effective in inviting him to the lesson. This prepared his mind and gave him the perspective that he could learn what we were about to learn.

I also caught my self when I was about to tell him something that was going to be revealed later.

{what could be improved}

I did not spend very much time in the invitation. While he still got the concepts and was able to successfully wrestle through the tensions during the comparison stage he had trouble articulating a few terms. I think if I have included some language about those term,s (digits) he would have named them rightly later on. Generally, it is recommended to spend close to 40% of the lesson in the invitation. I choose not to do that on purpose thinking that it was a super simple lesson and he was only taking a small step in this topic, but I see in hind sight that it still would have been better to take a little longer playing with decimal street and using some of the words I would have been using throughout the lesson. i.e. the digits situation…. :/

I think the main thing I could have done to extend it is ask more questions. There was a few times I told him something that I could have asked. Asking trumps telling on the part of the teacher in the mimetic sequence. I also could have asked him some narration style questions relating to everything place value and the decimal system.

I also told him to “not freak out about something” and I cannot recall why I felt the need to say that. I probably should not say that again.

{notes}

One thing I choose to do that there is some controversy on is that I named the logos of the lesson at the end of the invitation stage. It is a common thing to try and get the student to name it or at least wait to name it until the explanation or application stage. It takes a lot of trust, laid back mentality, and patience on the part of the student and teacher for this to work well. My son is not there. So telling him the logos of the lesson gives him a sense of where to file everything in his brain and keeps him on track. I have also noticed there is a connection between my growth in the mimetic sequence and I am sure as I become a better mimetic teacher the need for this will diminish. Therefore, currently, I include some definitions in my invitation stage.

Presentation

{what was done well}

I transitioned to this stage when I presented the number 413.

This went well for the most part. I had planned all my types out ahead of time and we moved through them smoothly. (planning ahead of time is the most important part here.)

{what could be improved}

I am still thinking about the comment Josiah made about them being overly simple. I wonder if that is okay to leave alone or if there is better way to handle those kinds of situations. I do not know yet, but am thinking about it. Maybe it just shoes he is ready to go the the Comparison stage if nothing else.

{notes}

N/A

At one point I told him that he needed to use a hyphen between two numbers. I could have asked about that, but technically that would have been difference lesson so I didn’t want to overwhelm him.

Comparison

{what was done well}

This stage began when I asked “What did we do each time we looked at a number according to its value?” I was really happy with this. Especially when I asked him to compare local value with regular value. You could see the wrestling through gap in this moment as he sought to synthesize this comparison.

{what could be improved}

I gave in to quickly when he didn’t name the definition of local/place value. He explained it wonderfully, but I wanted him to know the definition. I should have drawn out my questions and been okay with not being particular about the definition. In addition, I was distracted by the girls at the at same moment. So I think all of that contributed to that moment.

{notes}

N/A

Explanation

{what was done well}

This stage was one question: “Tell me the ways we can think about the value of a number” and “Tell me the ways we can express a number”

{what could be improved}

N/A, this is a pretty simple stage.

{notes}

During this lesson we worked on two different topics. We learned how we can think about a number according to value and we actually did the work of expressing the value in each of the three ways. Technically one could have 4 logoi for this lesson.

1. You can think about the value of a number according to its local/place value, its value, and its simple value.

2. You can discover the value of a number by asking how many units are in a given number.

3. You can discover the local value of a digit by naming the place it is in on decimal street and applying that to the number.

4. you can discover the simple value of a digit by naming it as thought it was in the units spot of decimal street.

(Decimal street is a concept Math-U-See uses to talk about the decimal system and place value. We do not use Math U See anymore but this has been the best idea ever to understanding place value. So we still use the terminology. Here is a video explaining it.)

I choose to mesh it all together because of the simplicity of the lesson for Josiah. He already knew it. I just needed to awaken him to some terms and a deeper thing about place value so he would have success in the next lesson. (place value into the trillions and beyond)

Application

{what was done well}

It was a fitting assignment for this lesson.

{what could be improved}

I should have had this printed or written out before the lesson.

{notes}

N/A

[box type=”bio”] If you have any question please ask them in the comments section below. Chances are if you are wondering about something regarding this lesson others maybe as well. Thank you for sharing![/box]