Three math problems per session?

How do you deliver math instruction to learners with a range of skills within the same group? The range I'm speaking about goes from adding two digits with no regrouping to calculating long division to using order of operations to solve equations. 

More importantly, 

why do we limit our group math instruction 

to just three math problems?

The Past

For the past 9 years, we've been posting three math problems on the board twice daily. But, we didn't always do this.

In 2010, we used problems from One Minute Math. This book featured 100 pages with ten problems per page. The focus was on getting comfortable with numbers, exploring mathematical relationships, and picking up speed. The problems in this book covered the range of concepts necessary to pass the lower-level TABE tests (Test of Adult Basic Education) and CCRS (College Career Readiness Standards). And, this book touted that these ten problems could be completed within one (or two) minutes. What was not to love about the math problems in these books.

We started by putting just five problems on the board. You know, giving us a thirty-second math warm up. 

What happened, however, was our group took thirty minutes to do five problems. After weeks of spending so much time on only five problems, we cut back to three problems. We reminded learners that these problems could be done in less than twenty seconds (after recording them in their notebooks, of course). Regardless, we took twenty minutes to do just three problems. Twenty minutes seemed like a long enough time to build and refresh concepts. 

The Point

We had to rethink why we were doing the math work on the board. What was the point? We determined that the point was not for learners to copy the problems from the board and then corner tutors to tell them how to do the problems. 

Rather, the point was...for learners to talk with other learners to get input from each other. Learners' tasks were to ask questions. Offer ideas. Explain decisions. 

We wanted to increase this behavior. So, we put the learners "on the spot." Or, should I say, in the spotlight. Learners took on the teaching role. One learner would go up to the board, select one of the math problems listed on the board, and then explain how to do the problem. We would all see, hear, and question the presentation. Other learners would explain (or teach) the other problems. 

The Result - watching or interacting?

We were looking for engagement that got learners to be in charge and in control of their learning. In this way, learners could take on the role of teachers. Tutors were just there to guide learners as they thought and shared and offer alternative ways of thinking. 

This teaching method - spotlighting learners as teachers - gave birth to engagement that included learners asking and exploring, "What parts don't make sense?" Group note pages were also outcomes from these teaching moments by these learners. 

The result? Learners of all levels were engaged - actively interacting, rather than just watching.

This instructional model was akin to the one-room schoolhouse. Lower-level mathematicians were exposed to higher levels of math. Higher-level mathematicians grew their understandings by explaining and interpreting questions. Win-win situation. 

How are you engaging learners

in your math program?

Reading-Writing: Free Scholarship Opportunity for the Mind

"Learning about what you don't know and then writing about it is akin to continuing your education on a scholarship." Marshall Krantz (1996)

Read-Write Connection

This line from Krantz's book Ideas and Research reminds me that reading and writing go hand-in-hand. I'm quite aware that reading and writing are cognitively diverse operations. Reading is about decoding symbols and connecting personal knowledge with the author's words to generate the author's intended message supported by the textual evidence. Writing is about composing ideas from personal, situational, and worldly contexts then transcribing them into words - articulating noises in our minds - that we must then conjure up appropriately-related symbols that eventually will convey the same thoughts as we intended them to mean. 

Mind Tools

My point is that reading and writing are tools of the mind - a way to process and share thoughts.

Often learners (and tutors) don't want to write because the process (especially spelling and grammar) seems cumbersome. And, writing always takes more time than talking. Writing, however, forces us to think and articulate our thoughts in ways that are very different than talking. 

Deep Thinking

My push is to get more people to think more deeply about what they are learning or want to learn and get them to record these thoughts on paper. 

Writing about what you've just read in your own words requires reflective thought. Time spent in reflection strengthens and deepens learning - creating and dedicating more synapses to the content and process of our intentional focus. 

What do you do to help you think 

deeply about what you are learning?

Motivation: Bookmarks

Keeping Agreements
Sometimes holding that agreement with ourselves is difficult. Don Miguel Ruiz reminds us in The Four Agreements: A Practical Guide to Personal Freedom (1997) that our self-agreements are the most meaningful and crucial as well as the easiest to slough off.

Even when we make commitments in front of a group, we can easily not follow through. We all know that what we say and what we do may be two different things. When we set goals with ourselves, do we really want that to happen?

Setting Goals
In adult literacy programs, we set goals. Learners & tutors set goals. We help each other make goals that are meaningful, actionable, and time-bound. We set one month goals. These goals often include learning a new skill, exploring a topic, completing a task, or finishing a book. 

Most of us, especially when the goals are not written down, forget the goals we make. We all need reminders. But, who wants someone nagging us to focus on the goal we set for ourselves?

Bookmarks
This past summer, we turned our goals into bookmarks - skinny pieces of card stock to mark a page in a book. Some of us put these bookmarks in the books we were reading daily. Some of us slipped them into the front vinyl cover of our 3-ring binder. Some of us posted them on our fridges or mirrors at home. And, we posted a set of them on our classroom bulletin board under our calendar. You get the picture - we put them where we'd see them to remind us. 

The bookmarks became the nagging voice that reminded us to focus - what's one thing I can do right now to move this goal forward.

As you can see from the bookmark at the top of this screen, each one had three parts. The top listed the person's name, career goal, and target dates. The middle section described the goal - the specific, measurable actions to be completed. The bottom section listed the way the person would celebrate. 

Did this strategy work? 
It worked for us. We had our highest rate of completion yet.

What are some things you do to hold 

your feet to the fire to get things done?

Speaker Jitters?!?

Photo by Robert A. Young

Remember the first time you had to officially "speak" in front of others?

Most of us are not comfortable, at least not in the beginning. Yet, presenting ideas in a group setting where everyone's eyes are on you is very much a necessary skill for work, home, politics, and society at large. The more comfortable you become, then the more likely people will listen and hear your points.

How do you prepare?

Tell us how you prepare for speeches in the comment section below.

Reflection

A quiet place to think about your day.

Reflection is an activity often ignored in our busy world. The closest many of us come to reflecting on our lives is in the minutes before we fall asleep. You know, those moments when we review our day, pulling up all of the negative conversations, happenstances, and images of our immediate past. Not a good idea.

If we listen to Carmen Simon in Impossible to Ignore, reflection supports long-term memory. Do we really need to remember all the insignificant, but emotionally-charged,pains of the day? Just to kick ourselves again for our behavior. Absolutely not. Unless, perhaps, we are working on ways to re/act differently next time.

We'd be better off if we use reflection to encode strategies and processes into our long-term memory. For example, over the weekend I made a blueberry pie with a new recipe. The pie was flavorful but far too juicy. The cooked blueberries tumbled out of the pie along with all of the juice. As I reflected on the process of making the pie. I realized that the recipe didn't include any thickener. Rather than lament on how poorly the pie held together, I reflected on the process and what to do in the future. I made notes in the recipe for future reference.

This same reflective process can be used for any action that we want to make accessible in our long-term memory. How does this work? Reflection is abut elaboration - connecting to the past, adding features, and identifying examples. The point is to build bridges and links in the brain so that we have more hooks in our brain to more easily retrieve or get information out of our brain. 

Reflection--thinking deeply about things--allows us the opportunity to build these synapses and strengthen retrieval. So, we need to take the time to think about the things we really want to remember, those things that will truly impact our future, rather than the negative moments.

Just before you fall asleep tonight, celebrate your successes and enhance the processes and strategies you want saved into your long-term memory.

Questions Facilitate Learning

Exemplary learning tasks engage
curiosities and foster growth.

Learning tasks guided by open questions posed after extensive resource building do not have singular answers. Engaged learners are expected to reflect on the question and bring to bear a combination of their experiences, problem-solving and reasoning skills, and specific content knowledge, strategies, and tools. These learners must sort through the language of the open question to find the essence of the question from which to explore their available resources and build their responses.

Exemplary learning tasks or open questions do just that - allow learners to explore, experiment, and explain their decisions based on their newly acquired as well as long-term knowledge, skills, and abilities.

What learning tasks stimulated and nurtured

 your knowledge, skills, and abilities? 

Consumption is not enough

"You go outside without clothes, you get arrested," Karl stated emphatically. To clarify Karl's point, Jesse added, "Arrested for not following social norms."

These summary comments were delivered after a brief discussion about three key ideas posed in Douglas Rushkoff's book Present Shock (2013): restlessness with anything that isn't "right now," balancing between virtual and physical worlds simultaneously, and skimming surfaces to make inaccurate connections.

Our conversation continued with the idea that society has many expectations. Most recently, this expectation seems to include that all of us must be effective and efficient users of technology. 

The question: "Can you use a computer?" takes on a completely new meaning these days. Being a passive consumer, like checking email or reading online news, is no longer enough.

We are expected to be producers. On the one end, we must pull together other people's ideas and share it with our "social set." On the other end, we must actively seek out information, share it with others, and add new and original thought that, even if for only a moment, grabs and engages the attention of other people. 

What have you produced today that will engage my attention?