Teaching students how to represent fractions on a number line can be tricky, especially when some fractions are represented on the same point.
The following scratch program helps students visualize this tricky concept – feel free to copy and modify the code if you find it useful.
For a course on teaching language arts, our final project was to create a fictional narrative on a digital platform – like a video or animation. After considering platforms like toontastic, which are easy to use but limit your creativity, I decided to take the plunge and try to use scratch for the story. The process was tedious, and the results are still not that polished. But the story below highlights the potential for scratch-based animated books that (with appropriate pauses and questions built in) could be used for “read-alouds” or even guided reading lessons (especially to build fluency).
Two weeks ago, I tried to use scratch (programming) to improve on the color-coded behavior management system in my pre-practicum class. The system currently in place is simple and easy to use; students start out as green (good), and can move to excellent (blue) or to yellow (warning – ineligible for leader responsibilities), orange (loss of recess), and red (parent conference):
However, I wanted to improve on this system by tracking behavior along specific dimensions, and using successful behavior along these specific dimensions (e.g. self-control or cooperation) to create a general color-coded behavioral assessment. To make desired behaviors more concrete and “game-like”, I also wanted to have specific challenges for students to “win”.
The result is an app with an opening screen that looks quite similar to the “analog” version:
But, after clicking on a “card” it becomes clear that:
When students successfully complete a challenge, balloons start streaming to reward them, and (after hitting the “r” key twice) their color coding changes as well.
Check out the live application at the bottom of this post, or click here (for the app on the scratch website), and please leave any comments (especially ideas to improve the app)!
Development notes:
Visualizing scientific concepts like magnetism and gravity can be fun, tedious, or somewhere in-between depending on your perspective. For early elementary students, it is probably hard to find a substitute for concrete models that demonstrate scientific concepts – like planetariums or fruit-models to communicate astronomical concepts.
However, digital simulations seem to have become realistic and interactive enough to be a reasonable substitute (even an improvement) over many traditional lab exercises – especially for upper elementary students and beyond (basically students who are well into the “concrete operations” phase and learning “formal operations”). And, the University of Colorado at Boulder has created a comprehensive, user-friendly, and most importantly – free – repository of these virtual models. I came across their site while trying to look for ways to help students visualize electrical circuits without a lot of set-up and clean-up, and have begun to rely on it for my own education. Hope you find it useful!
I’ll admit it – besides “knowing” that tides were caused by the moon’s gravitational pull, I had no idea why tides existed. A science teacher training class forced me to confront this ignorance starting with the simple question – if the moon’s gravitational pull causes tides, why do we have two high tides and two low tides in a day? (the moon’s orbit around the earth takes roughly a month, so tides should basically be dictated by the earth’s rotation – i.e. take 24 hours to go from one high tide to the next).
Digging deeper into the matter, I became pretty frustrated – online resources typically introduced another force (centrifugal force) to explain why the ocean “bulges” towards the moon (and sun, which is another layer in this topic), but it was hard to develop an intuition of how this all works together from the material that I found. Fortunately, people like Ingo Berg exist. His website has an application that finally helped me visualize the forces that shape tides – it might also help your students who need to construct visuals to understand concepts.
One of the main benefits of mathematics is the development of abstract reasoning skills. However, fluency – or the ability to immediately process simple calculations or recognize basic math facts – is also important to develop as students progress through elementary school. Just like being able to recognize words without decoding letters (“sight reading”) aids reading comprehension, fluency with basic math facts can help students master tasks that rely on more abstract reasoning. In other words, being able to automatically add, subtract, multiply, and divide single digit numbers frees up student’s mental resources (specifically their working memory) to focus on more conceptually challenging tasks.
And building fluency is an area where online tools really shine. Unlike a human teacher, online tools can continually and carefully monitor the performance of dozens, hundreds, or thousands of students – their error patterns, response times, and growth rates – and provide each student with material that is designed to boost their performance. One of these tools is xtramath – which allows teachers to tailor specific programs – like division, or subtraction of single digit numbers – to their students, then allow students to work for 5-10 minutes a few times a week to develop fluency. The icing on the cake is that the program is free for teachers and families. You can navigate to their website by clicking the image below:
Humans are naturally motivated to solve problems, especially problems that they can relate to. Unfortunately, most classrooms limit problem solving activities to word problems in textbooks, which students often cannot identify with. Prodigy is a Mathematics App/Website that develops problem solving skills by tapping into the intrinsic attraction that many children have to games involving quests, wizards, and battles. In the game, students have to answer progressively more difficult word problems to defeat wizards, unlock health and potions, and ultimately defeat a dragon. While many of the problems in the game are similar to ones in textbooks, the ability to the program to adapt difficulty based on previous answers, and rich context in the game still makes this game worth considering for elementary school children.
Students who are not yet “fully operational” or able to reason using abstract concepts, can still learn form mathematical concepts with support. They typically need to develop these abstract representations of concepts in three stages, using: 1) concrete representations (like a geo-board) ; 2) semi-concrete representations (like a drawing); and 3) abstract representations (like a formula). While concrete “manipulatives,” like base-ten blocks, are widely used and effective in introducing concepts like place-value, evidence suggests that “virtual manipulatives” can be similarly effective.
Toytheater has an excellent selection of “virtual manipulatives” that students can use online, including a realistic version on fraction strips or fraction blocks. The image below will take you to their website (in a new tab) where you can explore their fraction strip app, along with other virtual manipulatives.
Comments and suggestions are always welcome. Thanks for visiting!