Making Math Meaningful in the ESOL Classroom

By Sherry Lehane

Math in ESOL Coursebooks

Did you ever start a home do-it-yourself project and suddenly realize you were in over your head? Maybe you didn’t have the carpentry skills or the right tools to do the project? This is how I felt many years ago when I attempted to teach math to my ESOL learners, many of whom had very little formal education. On the surface, it seemed easy enough. The ESOL coursebook I was using had math tasks embedded in the units such as totaling a bill, comparing prices, reading pay stubs, and creating a budget. I would model how to do the math, we would practice doing a few examples together, and then students would be able to complete the activity. There was one hiccup in this plan–the level of math thinking was superficial. There were many embedded math concepts that could be explored, but I did not yet have the tools to teach them. The tools I needed included a deeper understanding of the underlying skills and knowledge needed for problem-solving and strategies for teaching math to students with a range of math and language skills. 

The Intersection of Language and Math

ESOL coursebooks include math activities because they are part of the life skills that we encounter daily, and it makes sense to include them in thematic units. We can help our English language learners navigate situations that involve math by integrating math into our ESOL instruction in a way that empowers them. In order to accomplish this, we need to dive deeper into math by creating opportunities for students to explore math concepts by using concrete objects and visuals, sharing their reasoning by discussing what they know and listening to the explanation of others, and ensuring they are able to transfer their knowledge to the real world. This is where language and math intersect! Integrating math in the ESOL classroom has the benefits of teaching learners math, language, and life skills all at once.

As a starting point, ESOL instructors can begin by thinking about the math they encounter daily or they can refer to the math activities in their ESOL coursebooks. Here is an example modeled from an ESOL coursebook where students are asked to compare prices of food items:

Happy Ketchup

K-Ketchup

$2.35, 20 oz bottle

3 for $6.99, 20 oz bottle

Typically, the accompanying tasks include reading labels and doing some computation such as: 

Which is the better buy? or How much cheaper is…?

In this example, students could use addition (2.99 + 2.99), multiplication(2.99 x 2) or division (6.99 ÷ 2) to determine the better buy. One way to extend learning and explore valuable math concepts is to allow students to first do the math and then share how they solved this problem. By listening to others describe their approaches, students engage in a productive discussion, work on articulating what they know, and begin to think critically — in this case, about why different operations work to solve this problem. This can lead to an understanding of the relationships among the four operations as the visual below illustrates.  

How would you explain the connection between division and subtraction? (Hint: Think about the connection between addition and subtraction as a starting point.) 

Traditionally, we think of finding the ‘right’ way to solve a problem, but in life, there are usually many valid options for solving a problem. The College and Career Readiness Standards describe mathematical practices of numerate adults. One of these practices, MP1 Making Sense of Problems and Persevere in Solving Them, addresses the ability to solve problems and explain one’s reasoning

Let’s look at another opportunity to expand learning using the same ketchup problem. Students might use the same operations such as division, but the algorithm, or procedure, might differ. Algorithms for division, multiplication, addition, and subtraction can be done differently in other countries. (Even math notation such as decimals, commas, and colons can have different meanings in other countries!) Discovering why different algorithms work is another teachable moment and lends itself to rich conversations and a deeper understanding of math algorithms. Here is a comparison of the U.S. and European algorithms for division. (Note: The European algorithm is used in many countries in Europe, South America, and the Caribbean.)

Differentiating for Math Ability

One of the challenges in any math class is differentiating instruction for math ability. Here are some ideas on how the Ketchup problem can be adapted for different math levels. 

More Accessible

To make the task more accessible,  change the numbers to whole numbers such as $2.00 and $7.00. 

More Challenging

For students who are ready for a more challenging task, you could add a step to this problem by adding a twenty-five cent discount coupon if you buy three or more bottles. Or you could modify the question by making Happy Ketchup a 22 oz. bottle. This would add ratios and proportional reasoning to the math task. 

Keep the Focus on Language Acquisition

In an ESOL classroom, a new language unit or theme is introduced with a personal question, visual, or situation that engages students in the topic and activates prior knowledge. The same can be done with math. Giving students a short word problem to do when they enter class is one way to engage them in the topic. Word problems that include math encourage students to talk about what they know and listen to the ideas of others.  This is also an opportunity for teachers to informally assess learners’ familiarity with the math concept.

Using the Ketchup problem as an example, teachers could post ads from flyers on the board and write up a word problem such as: You’re having a big cookout to celebrate the first day of summer. There will be about 75 people there. How much ketchup do you think you’ll need? Which is the better deal? 

Teachers can simplify the language or make the vocabulary and grammar more complex. The grammar focus can be adapted to whatever language structure you want to practice: comparatives, superlatives, question forms, conditional statements, and many more. This can be part of a shopping unit, a community event lesson, or a lesson about holidays and celebrations. As with any topic, think about the vocabulary, including math vocabulary, when planning the lesson. 

The next step is to decompose the tasks – a process with which ESOL teachers are familiar.  Both ESOL and ABE teachers need to determine what the embedded concepts are that students will need, and how they can explore them in order to gain a deeper understanding. This deeper understanding is how we can empower our learners and give them the language, math, and problem-solving skills they need in daily life, higher education, and the workforce. 

Continued Learning

Are you interested in learning more about strategies and resources for teaching math and numeracy skills in ESOL context? TERC, in partnership with the EdTech Center @ World Education, offers several online courses, including:

  • Mathematizing ESOL I: Integrating Whole Number Operations
  • Mathematizing ESOL II: Integrating Benchmark Percentages and Decimals
  • Mathematizing ESOL III: Integrating Ratio Reasoning

Contact sherry_soares@terc.edu for more information about the courses above and other professional development opportunities.

 

About the author: 

Sherry Lehane has worked in adult education for over 20 years, teaching ESOL and digital literacy to adult learners. She is a strong advocate of integrating numeracy in the ESOL classroom. In recent years, her work has focused on supporting teachers in integrating math and technology.  She has co-created several resources designed to help ESOL teachers integrate math including several online courses and ESOL math packets. In Rhode Island, she coordinates the activities of the Rhode Island Tech Hub for Adult Education, which is the professional development provider for the use and integration of technology for teaching and learning.  

Exploring Economic Inequality with The Change Agent

AEFL Week LogoExtreme inequality in terms of wealth and income is barely news anymore. CEO pay has skyrocketed over the past 30 years while workers’ incomes have stagnated or decreased. A report from last April states that the world’s “richest 64 individuals control as much wealth as the poorest 3.5 billion people combined.” Five years ago, the occupy movement exploded onto the scene, and now “the 1%” vs. the “99%” are commonly accepted ways of talking about the extremely wealthy and the rest of us.

Most students will not be too shocked by the first three articles in the lesson packet titled “Making Sense of Extreme Inequality.” (Click here and scroll down to Lesson Packet #9.) The first, written by a learner from Hartford, CT, talks about growing up on cornflakes and rotten meat. She ate more when she got a job at McDonald’s, but then she gained 40 pounds. The second article, “Redecorating in a Recession,” shares a list of the pricey items a CEO used to decorate his office at a time when the economy was tanking and his company was laying off workers. The third article by a learner in Methuen, Massachusetts, talks about how hard it is to stay mentally and physically healthy when you’re struggling to pay the bills.

These highly accessible articles provide the scaffolding to a more complex piece, which many people may indeed find surprising, as it busts some of the fondest myths that help prop up extreme inequality in the U.S. Andy Nash’s article, “Nobody Makes It on their Own,” is a more challenging read, but students will be primed to take it on because it puts the stories they just read in context and provides some explanation for how the rich keep getting richer.

Why teach about extreme inequality? Isn’t it just depressing? Yes and no. Yes, for obvious reasons. And no because this catastrophic imbalance is not written in stone. It came about due to policies, and it can be changed in a similar fashion. (What are some ways it can it be changed? Check out a lesson packet titled “Taking Action at Work.” Click here and scroll down to Lesson Packet #10.)

Students in adult education programs have everything to gain from understanding that poverty and inequality are not handed down from on-high. Education can boost individuals’ chances. Addressing macro-economic policies — including more progressive taxation and less corporate control over public decisions — boosts everyone’s chances.

http://changeagent.nelrc.org/

Defining Work Readiness

Introduction

Adult literacy has been at the heart of World Education’s work since it was established in 1951 in India and founded the Literacy House upon the urging of Mohandas Gandhi. Sixty-four years later, while gains have been made in many parts of the world, the need for literacy education remains great:  there are nearly 800 million adults and out-of-school youth in the world with limited or no literacy and numeracy.  In the U.S., adults’ basic skills are falling behind those of other developed nations.  For the first time, the skills of young adults are lower than those of their parents’ generation.  At the same time, people need even more different types of literacies to move ahead in their lives than in 1951. World Education’s approach to literacy education and how we define it has evolved and expanded commensurate with the skills adults need to navigate systems, pursue opportunities, and address problems successfully in their personal lives, work, and communities.

To commemorate the Adult Education and Family Literacy Week, in this series of blog posts World Education/ U.S. staff share their views on what literacy means to us today and how we are helping to advance adult education in multiple ways.  Our list is not comprehensive: there are not enough days in a week to feature all the types of literacy youth and adults need in today’s world!  Please join the dialogue.


Workplace Literacy

Adult learners often seek to improve their basic skills because they want better jobs. And as adult educators, we want to provide them with the skills they need to get those jobs. But what if there are simply not enough good jobs to go around? Do we proceed, happy that at least a few will procure that “better job”? Or do we help our learners gain the skills they need to turn bad jobs into better jobs?

The fact is: there are a lot of really bad jobs out there, and the bad jobs are growing the fastest.

According to the Bureau of Labor Statistics, the 30 occupations adding the most jobs from 2012 to 2022 will add more than 15 million (15,628,000) jobs. (See chart below.) Yet only eight of these occupations will pay a living wage, which the MIT Living Wage Calculator puts at $20.17 per hour (or $41,593 annually) for an adult raising one child.

What about the other 22 jobs? They pay less than a living wage, some of them just barely above what the U.S. considers a poverty wage. Workers in four out of the top five of the fastest growing occupations (personal care aides, retail salespersons, home health aides, and food preparation workers) can expect to make just a few thousand more (about $20,000 per year) than a poverty wage.

As adult educators, how do we let these facts inform our teaching and our understanding of “work readiness”?

At a recent conference where I was sharing these facts in a workshop, one teacher said, “I don’t want my students to see those statistics!” Right. Think how discouraging it would be to find out that all this work you are doing to get your GED or to get into college is not necessarily going to yield a decent job!

But if we pretend that this is not the reality, then we are doing our students a disservice.

If it is true that millions of the new jobs that will be added to the economy over the next 7 years will pay less than a living wage and will offer little to no advancement opportunities, then we must re-think the idea of “work readiness.” Does it mean gaining the skills you need to take your place in a low-paying, dead-end job? Hopefully not. The definition of “work readiness” should be expanded to include equipping learners with the knowledge and background they need to see themselves as advocates for themselves and others. In the classroom, our job is not just to shape students to meet the needs of future employers. Of course we want them to have the basic skills and the technical skills they need to find decent work. But we also want them to be able to shape the kind of work that is available as well as the terms of their employment, including compensation and benefits.

Adult student contributors to The Good Jobs issue of The Change Agent wrote thoughtfully about their hopes and ambitions for work. They want jobs that allow them to support their families, that provide dignity as well as a paycheck, and that don’t leave them thoroughly exhausted and stressed. Mariama Diallo in New York City doesn’t want to be “paid today but broke tomorrow.” Maria Hernandez in Fayetteville, Arkansas, wants to be treated like a “human, not a machine.” Carwasheros, grocery store workers, and hotel and restaurant workers all over the country tell stories about fighting for their right to organize, recuperating lost wages, and winning dignity and respect on the job. They are using the support of labor unions, community organizations, and workers’ centers. Students see that the reality is more complicated than just acquiring basic skills and credentials. They also need to know how to advocate for themselves and others so that they can leave our classrooms with the skills they need to join with others to affect the job market, not just be delivered into it.

Occupations with most job growth chart

 

Using the Technology Issue of The Change Agent to Teach to the College and Career Readiness (CCR) Standards

World Education Transition to College

The Change Agent has heard from teachers and programs that they need materials to help them teach to the new College and Career Readiness (CCR) Standards, and we have engineered our lesson plans and activities accordingly.

For example, turn to the story called “Finding Felix” in our latest issue, and on the surface, it is simply a moving account of a young woman who used social media to find her long-lost brother. But by using the carefully designed activities we have included, your students will have the opportunity to work on anchor standards 1-3 of the CCR standards in reading as well as writing. These include being able to determine what the text means and how you can prove it, and being able to write in various ways in response, including providing reasoning, evidence, and details.

Look on page 3 of the Technology issue, and at first glance, the story is a moving plea from a father: How can he afford to buy his daughter that fancy smart phone? But it’s not just a highly relevant account of a problem that almost every parent can relate to, it is also an opportunity for students to work on anchor standards 1-3 for speaking and listening as well as 4-6 for language. These include being able to converse by expressing yourself and building on others’ ideas, and being able to independently build your vocabulary. The online audio version of this article, available to subscribers, gives students a chance to listen to the article while they read along (an evidence-based strategy for improving reading comprehension, as well as grammar and pronunciation).

If you’ve been hearing a lot of buzz about the new “Common Core,” and if you’ve been wondering what resources are available for bringing that work into the classroom, you should know that The Change Agent lends itself rather seamlessly to the key shifts in the new CCR standards. What are those shifts? In English Language Arts, they can be summarized as: 1) expose students to increasingly complex texts, 2) give them opportunities to analyze readings and be able to cite evidence from the text for their analysis, and 3) help them build actual knowledge in science, history, and technical subjects.

The Technology issue of The Change Agent (published September 2013) is filled with extensions, factoids, background details, and research opportunities that help students build knowledge in exactly these areas (see #3 above). Discussion questions and writing prompts send students back to the text to find out what the author said, why she said it, what she meant, and how you know that’s what she meant. Articles reference each other and build on each other, offering a built-in “staircase” to more complexity and more knowledge. Opportunities to practice grammar and vocabulary exist within content that is interesting and relevant to adult learners. Not only that, but most of the content is written by peers, so readers have role models on every page! Look at pdf of the table to see which articles address which standards.

The Change Agent has a long history of using socially relevant material to teach reading, writing, and math. With back issues on everything from fashion to health to the economic crisis, our articles impart knowledge, and the lesson plans and extensions help students distinguish fact from opinion, build their knowledge, assess the author’s point of view, analyze evidence, and build math skills based on real-world problems. So if you’re already using The Change Agent, you’re a step ahead when it comes to teaching to these standards. And if you’re not using The Change Agent, consider subscribing. It costs just $20 per year to access the current issue, all the back issues, and all the online audio and issue extras.

Adapted from “College and Career Readiness Standards for Adult Education,” Susan Pimentel, 2013; and with thanks to www.teachingthecore.com.

Photo credit: Jon Crispin