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.
One in ten students in MA is classified as an English Language Learner (ELL). And most of these students struggle to perform at the same level as other students on measures of academic success such as standardized tests and high-school completion rates. In theory, translation technology could help ELLs learn in Sheltered English Instruction (SEI) classrooms by helping them access knowledge that they have in other languages. The following presentation summarizes my efforts to “translate” theory to practice in an SEI classroom during my full practicum. Drop a line if you have comments or questions!
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.
Why do people migrate, and how does the process of migrating effect people and countries?
Grade Level: 2
Duration: 2 lessons, 45 minutes each
Supporting Questions: How has immigration shaped the U.S.A.? How long does it take for a new country to feel like home? In what ways do immigrants change after they move? In what ways do they stay the same?
What Students Will Produce : By the end of the lesson, each students will have completed a 3-part graphic organizer that they will use to guide their future work.
What Students Will Learn: Through a guided reading activity, jigsaw activity, and self-directed research, students will develop and demonstrate understanding of migration as a process that: 1) has shaped the U.S.A. 2) results from a variety of causes; and 3) involves a process of adjustment that can be unique to individuals.
Before Lessons: Gauge student familiarity with and attitudes towards migration/immigration. Also identify understanding of essential vocabulary for the lesson, including: immigration, migration, process, adjustment/adaptation/assimilation.
Opening: Ask students if they know where pizza came from. Then, use this article to connect immigration to something that students are familiar with. Extend to other foods, sports, and other student interests (like Google being founded by immigrants).
Whole Class Reading: Lead the class through a reading of Faith Ringgold’s “We Came to America”, pausing after each page to connect the book to students’ background knowledge (of indigenous people, slavery, refugees, and personal knowledge of immigrants). Take time to analyze the art as well – for clues about geography, historical context, and the nature of the migration. Give students time to start filling out their graphic organizer after the reading.
Jigsaw Activity: Divide students into initial groups to view/read one of several stories of young people who immigrated to the U.S.A. (link). Facilitate student group discussion, and give students time to work on their graphic organizers in their initial groups. Then mix up students from the initial groups to form new groups that consisting of students who have learned about a unique immigration experience so that students can compare notes (using graphic organizers for support). Provide time for students to add information to their organizers.
Self-directed Exploration: Provide students time to go through a list of curated content on this own. Once again, ask students to continue updating their graphic organizers. Here are some starting points:
What is a refugee by Elise Gravel
All the way to America: The Story of a Big Italian Family and a Little Shovel by Dan Yaccarino
Interviews with young immigrants
Website about immigration for kids
Closing: end the lesson by introducing the final product that students will be creating, and connect the project to what they learned in the past two lessons (for example, they will be documenting someone else’s experience immigrating, just like the stories/videos the students learned from). Explain how the project will work using a visual representation of the process (on a board, for example), and refer back to this visual throughout the unit.
Massachusetts Social Studies: MA 2.T3 “History: Migration and Cultures”
C3 Social Studies: D2.Civ.10.K2 “Compare their own point of view with others’ perspectives”
Websites
Books
We have a cupcake recipe for only 1 person, but more people are coming to a party. And…the cupcake recipe has fractions. Most people know how to add and multiply whole numbers like 3 x 3. But 1/3 + 1/3???
Your mission, if you chose to accept it: Modify the recipe below to be enough for 4 people, and show that you have the right answers using fraction strips. The party hosts need to know how much stuff to buy. And they don’t want yucky cupcakes!
This mission is important, so you need to train. I have made many cupcakes, and will be your guide. Here’s what you will do:
First, get to know your team. Ask each other about their favorite food, and if they have ever baked before. Also, ask each person what he or she knows about fractions. All this information will be useful later.
Second, learn how to use fractions strips (click the link below). These will come in handy if you have to prove that you’re right.
Third, click the button below for a handy-dandy worksheet to do a training run with your guide (that’s me). We will change the recipe to be for 2 people and use fraction strips. We will practice changing the recipe and proving we’re right.
Use the handy-dandy worksheet and the fraction strips to modify the recipe. Sometimes the number of people at the party changes. So be prepared to change the recipe amounts.
Work together in your teams. Make sure all team members agree with your answers.
Return to base when you have completed the mission for debriefing. Your guide will come along in case you have any questions.
Now for the hard part. The boss will want to make sure your recipe is correct. Use the fraction strips or any other tools you have to convince him that your cupcakes will not be yucky. Good luck!
Many of us probably memorized the slope intercept formula (y=mx+b) in middle school without fully understanding how the formula represents linear growth. I was not able to visualize how the formula translated into lines until 11th or 12th grade.
It turns out that, in Japan, some teachers give students an open ended (but supported) problem called the “growing dot” problem to try and build conceptual knowledge that relates to the slope intercept formula. Check out the slideshow below (adapted from a presentation for a Math and Technology class at Boston College) to see how one teacher applied this method to his middle-school students.
Source: Goldsmith, L. T., and Seago, N. M. (2013). Examining mathematics practice through classroom artifacts. 88-96, Boston. MA: Pearson
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:
