Here’s something we found online that seems like a good math resource for adult education practitioners:
Check out this article/lesson plan from Patrick Honner in the New York Times:
N Ways to Apply Algebra With The New York Times *
In this article/lesson plan, Patrick shares some real world applications of math that can be investigated using information in the New York Times (or many other newspapers), such as:
- Mathematically Modeling Mortgages
- Ranking and Evaluating Colleges
- Calculating Car Costs
- Algebra of the Election
- Olympic Algebra
- Solving for Stocks
All too often workbooks teach the algebra embedded in these examples with a “one-right-way” plug-it-into-the-formula process. The examples in this article foster a much more open ended, problem-solving approach to applying Algebra in real-world settings.
This approach fosters the development of algebraic thinking, not just the short-term ability to plug numbers into formulas. As we stated previously:
Algebraic thinking involves recognizing and analyzing patterns, studying and representing relationships, making generalizations, and analyzing how things change. It is about making predictions based on patterns or relationships, making decisions, and solving real problems. It is about creating models based on phenomena that occur around us. Donna Curry (emphasis added)
What creative and innovative approaches have you used to teach these traditionally ‘formula-based’ algebra problems? What other types of meaningful real-world applications have you used in teaching algebraic thinking?
*Part of The Learning Network: (Teaching and Learning with the New York Times)
Have you recently found something interesting ‘in the news’? If so – let us know at firstname.lastname@example.org.
It seems like contextualized instruction is getting a lot of attention lately, especially when the topic is basic skills instruction that helps adults along “career pathways”. Let’s take a closer look at this idea.
Q: So, what *is* Contextualized Instruction? And what would it look like in an Adult Education class?
A: In adult education, the term “Contextualized Instruction” describes a set of teaching, learning and assessment practices that:
- are aimed directly at developing the skills and knowledge that adults need to deal with specific situations or perform specific tasks, and
- that they have identified as important and meaningful to themselves “right now” in their everyday lives.
In addition, rather than focus only on the possession of basic skills and knowledge, contextualized instruction focuses on the active application of those skills and that knowledge “in a context”. (And this context should be as “real-world” as is feasible.)
Q: OK, this sounds familiar – is Contextualized Instruction a new idea?
A: No, in fact, it is not a new idea.
Early in the 1990’s, a report from the Secretary’s Commission on Acquiring Necessary Skills (SCANS)1 stated that acquiring job-related content and basic academic skills is not enough to prepare adults and youth to be effective on the job. Just as important, it said, are interpersonal, decision-making, and planning skills along with the knowledge of when and how to apply these skills within the context of the workplace. This same report indicated that teaching these skills would require instructional approaches that focus on cooperative learning, apprenticeship models, and teamwork.
The 1990’s also produced some sound research about the importance of teaching basic skills “in context”. This cognitive research (about how people learn and develop expertise) showed that knowledge learned only at the level of rote memorization rarely transfers from one context to another.2 With the way that most people’s brains work, it just isn’t effective to first teach skills and knowledge separated from their context, and then hope that learners will end up knowing how to transfer what they have learned to life outside the classroom. Instead, learning will transfer more effectively when learners:
Think of a challenging speaking or listening task you’ve accomplished lately.
What did you do to try to plan for or get through this task?
Now consider, what kinds of listening and/or speaking tasks non-native speakers may find challenging.
Would the approach you used in the above situation assist them to communicate effectively for any of these tasks? Which ones?
As educators, we are often encouraged to teach ‘strategies for reading‘ to our adult learners, as well as ‘strategies for writing‘ and even ‘strategies for solving‘ various types of mathematical problems. But we don’t hear nearly as much about teaching specific strategies for listening or for speaking to our adult learners. What strategies should we teach? and how?
For most of us, listening and speaking is something we do repeatedly throughout every day. Thus we often take these skills for granted – unconsciously implementing important strategies that help us to communicate with those around us. When a speaking/listening task is more challenging or more critical, however, you are likely to slow down and think through how to handle it – engaging in strategic thinking. Language instruction expert Andy Nash provides an example and some information from the research:
…I know how to monitor my comprehension when I’m listening – I am skilled at checking that things make sense, asking for clarification, taking notes, paraphrasing, etc. But I don’t always use these skills. I may let my mind wander and lose track of what’s being said. However, if I know the speaker is going to be talking about something that really matters to me and that I’m prone to drifting off, I may think ahead about which of my skills I’ll use in this situation. I might plan to take notes or sit up front to stay focused. My skills then become purposeful strategies that I’ll use to make sure I understand and remember what I hear.
Studies have found that good language learners are aware of the ‘communication strategies’ they use and are skilled at matching these strategies to the task they are working on. For instance, good learners know that if they lose the meaning because someone is speaking too fast, they need to use a ‘repair strategy’ that will solve the problem (e.g., asking the speaker to slow down) in order to regain their understanding.
Less strategic learners, like many adult ESL students, may be aware of being confused, but may not know what to do, or may choose a less effective strategy (e.g., asking for repetition, which may still be too fast). Less able learners tend to use what communication strategies they do know in a more random, unconnected, and uncontrolled way (Chamot, 2005).
Many contemporary textbooks give students practice with strategies, and even provide some steps to follow. They may include activities such as this one on the ‘Prediction’ strategy for listening:
- Predict what you will hear the speaker talk about.
- Take notes as you listen.
- Now compare what you heard to your predictions.
Such an activity is intended to give students practice with prediction strategies. It assumes, however, that learners will appreciate the value of this language strategy and transfer its use to real-life communication situations outside the classroom. Research finds, however, that transfer cannot be assumed (Bransford, Brown, and Cocking, 2000). Without explicit discussion of why the strategy is useful or how and when to adapt the strategy for use in diverse real situations, application does not usually go beyond the classroom walls.
Understanding that proper strategy use is contextualized – that it will vary by situation – is key to students’ ability to apply strategies to real life tasks. It is not enough to simply present a strategy and have students practice it during academic tasks. Instruction must explore how that strategy will be applied in a variety of different real-world activities – or contexts – in order to be sure students can use the strategy to meet varied communication purposes.
While Andy was specifically addressing the needs of non-native speakers of English (ESL learners), her points could apply to many of our native-speaking adult learners as well. Effective listening and speaking – communication – skills are critical components of success in both post-secondary and workplace settings. And basing instruction on real-world situations – contexts – is an effective approach for any subject.
Please share with us your thoughts on strategies for listening and speaking – its importance both in and outside the classroom, how you address it, any ‘ah-has’ you’ve had, etc. Below are some questions Andy poses to get you started:
- What strategies for listening and/or speaking do you currently teach your adult learners? How do you teach these strategies (what examples or approaches do you use)?
- Have you ever talked with your students about the strategies they use when they communicate? If so, what strategies do they describe using? How do these compare with your own?
We look forward to reading your thoughts and experiences.
Learn more about teaching listening and speaking strategies in the EFF online mini-course, Teaching Listening and Speaking Strategies in Adult ESL, or via other EFF professional development materials/services!
Research cited in this post:
Anna Uhl Chamot (2005). Language Learning Strategy Instruction: Current Issues And Research. Annual Review of Applied Linguistics, 25, pp 112-130.
Bransford, J. D., A. L. Brown, and Cocking, R.R., eds. (2000). How People Learn. Washington, D.C., National Academy Press. Available at: http://www.nap.edu/openbook.php?isbn=0309070368