Artifacts From This Week:

I think my favorite thing this year will be collecting the work that these students do as they solve problems. So far, it’s completely fascinating. This week was addition & subtraction – here are some artifacts from the week:

This last picture is fascinating to me:

The red and green work are subtraction problems without borrowing, which this student got incorrect. The blue and yellow problems are subtraction problems with borrowing, which the student got correct. So somehow, in trying to create a visual intuition about subtraction in order to motivate the concept of borrowing (which looks like it was a success), I un-taught this student their original intuition for subtraction without borrowing. I guess we’ll work on this next week.

Next week is multiplication. Some students know their multiplication facts already; some students have no idea where to start. It’ll be a curious week.

Some Khan Academy Things

I’ve got a Wall of Champions – Khan Academy Version going in my classroom:

Some notes & clarifications:

• I only use Khan Academy for the exercises – we don’t watch the videos, and I don’t really want my students to either. However – the ‘hints’ that are provided for each question are the most useful for my students in terms of feedback and learning a process on their own. Some students, when they see something they don’t understand, display all of the hints and then follow through the problem to see how it was solved. I have two students who  have started displaying the entire hint text, then copy and pasting the text into Google Translate, then reading the explanation in their native language. Another neat feature of Google Translate is you can highlight particular words or phrases and it’ll show you the corresponding word or phrase in the other language. So if a student sees two unfamiliar words in English (like numerator and denominator), then sees unfamiliar words in their language – they don’t have to guess which word is which: google translate will highlight the text and they can know for certain.
• That last bullet points is too long. A shorter way to have said that is: we don’t use Khan Academy videos for instructional purposes ever. Some students watch them because they want to learn the English, not because I want them to learn the math. However, the hints in the exercises have much more instructional value, especially when paired with Google Translate.
• My kids are really enjoying the structure of the Khan exercises – the isolated skills and repeated problems, that they have positive reinforcement and some gamification elements, that they can compare their progress with others, that they have tangible goals and intangible rewards, and that they can work at their own pace despite the clear language barriers.
• I am also really enjoying the structure of the Khan exercises because it takes a lot of the management of a differentiated classroom out of the picture, letting me focus more on helping the students who need the most help and need things taught at a fundamental level, while letting the students with a strong mathematical background progress at their own pace and help each other out.
• I wish Khan Academy wouldn’t consider a skill ‘practiced’ if they get the very first problem correct, even though I understand the intent of allowing students to move quickly through content they already know. I wish it was ‘first 2 correct’.

Something that’s been fun for me is: the goal is to eventually prepare these students to enter an Algebra I class once their language and fundamental skills catch up, which means I’m basically teaching a condensed 3rd-8th grade curriculum to a group of motivated, intelligent students – and, since I know how things in 4th grade (like multiplying multi-digit numbers) connect to things in high school (like multiplying binomials), I can be very purposeful with how I present certain topics and how the ground work is laid for future conversations (like using the box method, which can be used for both skills). Most traditional students have to wait almost a decade before this connection is made. My ELL students will have to wait a year at the most before this connection is made – a much shorter amount of time – and I’m curious how the ‘quickness’ of this connection will effect how well they internalize the concepts.

Paging Christopher Danielson

I just want to put out there that, of all the potential people who read this series and react to it and have feedback or pushback, Christopher Danielson is someone whom I am most interested in hearing from (he’s already provided some neat insights that I’m looking into). I’m positive that many of the problems and solutions and strategies that I will end seeing this year will overlap almost entirely with the same problems and solutions and strategies that one would see when presenting mathematics to a child for the first time, which is one of several niches that Chris is a part of (Have you seen Talking Math with your Kids?). The thing I’m curious about is: if/how these strategies break down as I adopt them for my ELL demographic. Next week, as I teach an older ELL student (with broad experiences in the world) how to represent multiplication for the first time, can I do it the same way I would for an English-speaking child who is learning multiplication for the first time? The nuances of this situation, if they exist, are curious to me.

The End