An inordinate number of kids are growing up without learning their multiplication facts.  Some of this is due to the prevalent use of calculators.  Some is due to the fact that there’s been an overall rejection of rote learning – throwing the baby out with the bathwater, in this case, I think.  Some of it is due to low numeracy as a result of math disabilities. 

         Many kids with learning disabilities really struggle with numbers and their values.  And, I think, it also has to do with processing memory and retention of information that isn’t used on a regular basis.

         I think there’s a place for rote learning of math facts in a demanding classroom.   The only way to learn multiplication facts and what happens when you add ten to a number is to recite them over and over in some way or another. 

         The way I use is skip-counting.  Skip-counting can be done starting at any age, and should continue to be done if not daily, then at least several times a week once the kids know the routine.

 I cannot stress enough the importance of visual cuing when it comes to math.  In this case, a giant number line, or individual number lines to 100 for each student are  in order.  You can also use individual multiplication charts or a giant one; the point is that the kids have to have the numbers 1-100 in front of them when they are skip-counting, at least during the first few months.

           A lot of teachers practice skip-counting with their students through 3, 4, and 5 multiplication facts, and then stop.  As a result, many kids know their multiplication facts through five, and can’t go higher.  Don’t let this happen.

         It can be a part of your daily routine to start with 3, and have the kids skip-count to 60.  Move to 4, then 5, and 6.  Once they know those, move to 7 and 8.  Practice them religiously.  I like to point at the numbers on a chart or number line with a pointer or a yardstick at first, but later it becomes a favorite reward for a student to be allowed to stand at the front of the class and cue the numbers. 

         It doesn’t take long for kids to internalize the facts as they continue to skip-count regularly.  But here’s the deal:  You can’t stop here. 

         One mistake I’ve seen over and over again is special educators working on skip-counting with their students and then never extending the skill into actual math problems.  And when I say “actual math problems,” I don’t mean a standard multiplication worksheet.  I mean math problems that require critical thinking.

         There’s no point in rote learning unless the information learned by rote is applied in complex situations.  Skip-counting alone, in a vacuum, has little meaning.  We need our students to be able to use the math facts to solve word problems, to reason through division problems, to figure out the value of x, and to  calculate prices and amounts. 

          So teach the multiplication facts by rote, but then require your students to use them, and use them in a variety of ways.  Only in this way will they truly be learning.

          In a demanding classroom, rote memorization has a place in supporting mastery of facts to be used in deeper-level situations.

         Kids with expressive and receptive language deficits need to learn how to use and understand words.    The speech section of the brain is an amazing thing, and synapses can be created, formed, and reformed without medical intervention.  It is by using and reusing words, practicing them in different contexts over and over again, that our students can overcome, or at least significantly diminish their language disabilities. 

         One of our favorite ways in the classroom is to play Jeopardy.

          I use Jeopardy games primarily for Social Studies, but it can be adapted for any content area.  All you need is some sort of board (I took a large portable bulletin board or white board, covered it with contact paper, and it can stand on an easel quite easily), a document camera, those little envelopes they put in books at the library (or laminated construction paper envelopes you affix to the board), and index cards. 

         I keep five columns of four card slots each on the board at all times.  Then I can switch around the categories and the answer cards with ease.

NOTE:  Our school district is putting smart boards, or Promethean Activboard smart boards in all of our classrooms.  (Lucky us!) This is going to change the way I do Jeopardy because I can set up a Jeopardy game right on the computer and work with it on the smart board.  But I haven’t done that yet.

         If you’re not familiar with the television game show, Jeopardy, it’s essentially a trivia game where the answers are provided and the contestants have to formulate the correct questions.  In a demanding classroom, we play Jeopardy at least once a week, sometimes twice, depending on where we are in a social studies unit, and our games last anywhere from 40 minutes to an hour and a half, depending on how much fun the kids are having.  And they have a lot of fun.

          All of the “trivia” in our games consists of information from our current social studies unit. 

TIP:  As the year goes on, our Jeopardy game may expand to include prior units.  Thus, at the end of last year, one category was about ancient India, one about ancient China, one about ancient Mesopotamia, and on category was just about vocabulary related to history.

         Most of the time, the categories are something like this:  geography, lifestyle, religion, leaders.  But that is not cut in stone; we often have a vocabulary category, one on military matters, one about trade, one about inventions.  It just depends, as I said, on where we are in the unit.

          I will preface my description of the game by saying that you should not have high expectations at first.  At the beginning of the year, students will just not do very well and will need lots and lots of coaching and extra time.  Even later in the year, in the early part of a unit, kids just aren’t as familiar with the facts as they will be.  What’s amazing is that within a matter of a day or two, the kids are really learning, integrating the facts, internalizing the information, which is better than simple memorization.  And did I mention they are having FUN?

How do I know this?  Because years later, my students are able to discuss with ease historical facts and ideas and concepts that they learned long ago in our classroom.  My student teacher, on a tour of the school by one of my students this year, was treated to a long description of  prehistoric humans and the development of key concepts including domestication of animals and plants, inventions of new tools, and ideas about religion and nature.  Another of my students from years ago recently texted me that he got an A in world history in high school because he had so much background knowledge from our sixth and seventh grade history class.

         Jeopardy is played, at the beginning, with teams of two or three students.  You’ll find that as the year progresses, many students want to play alone, and others will still want a partner.  This is fine.  It’s great, even.  And you’ll be amazed at who emerges as the stars of the game, confident in their ability to formulate correct questions properly.

         I have prewritten the answers on index cards and put them in the slots or envelopes on the Jeopardy board before we begin. (when the kids see me changing the cards earlier in the day, they get excited knowing that we’re going to play – they really look forward to it.)

          The first team picks a category and an amount (I have 100, 200, 300 and 500 points as our amounts, but you can use any numbers you like).  I pull the appropriate card, and show it under the document camera.  (This is a big help to those kids who are visual learners and need to see the words of the “answer,” not just hear them.)  I remind the team to put their response in question form.  I don’t use a timer, because I want the kids to feel pretty relaxed as they figure out their response and put it in the proper words.

 An example of an “answer” might be:  Wheat and barley.  The proper question could be:  “What grains did the ancient Mesopotamian farmers raise?” or “What are two grains domesticated by Mesopotamian  farmers?” 

         Periodically, I do a mini lesson or reminder lesson about clues we can use to determine the question form.  Sometimes, the kids need reminders, for example, that an answer that contains a date needs a question that starts with “when”, or that a location implies a “where” question.  Often, however, I’ll catch kids coaching each other on this, even if they are on different teams.

         According to our former Speech Language Pathologist, the effort of thought it takes the kids to use the answer/fact to form a question is a challenge that results in significant improvements in their speech skills.  We’ve noticed a huge jump in confidence, mastery of facts and concepts with great ease, and a terrific increase in use of rich vocabulary and complex sentences.  

         We also have a classroom full of history buffs, who are proud to demonstrate their mastery and expertise  both orally and in writing. 

          In a demanding classroom, kids talk about information in a variety of ways instead of just repeating back what we tell them.

         I’m teaching a general education math class this year that includes many of my own kids with learning disabilities as well as kids who do not have IEPs.  We’re  about six days behind the other class at the same grade level, and both of us finished the first two units well before the district’s first math benchmark assessment. 

          Greg Roy, my general education colleague, has, as I have said before on this blog, taught me a great deal about math and math instruction.   He and I disagree about mastery, by the way, but that doesn’t impair our ability to collaborate.   He moves at his speed, and I move at a different one,  but we’re both moving forward.

          Anyway, Greg’s a proponent of math routines, and he does them at the beginning of the day as well as at the beginning of a math class.  Routines are great, for several reasons. 

          • First, they provide kids with ongoing practice of previously-learned skills.  My routines always have problems from lessons we have worked on since the beginning of the year – usually types of problems the kids struggled with mightily, so that the skills will become firmly embedded. 

(A recent math routine had a word problem involving adding negative numbers, 2 fraction simplifications, 1 changing from mixed fraction to improper fraction, 1 changing improper fraction to a mixed number, and 2 dealing with multiplying decimals by 10, because my kids bombed that area on the last unit test for some reason, as well as a problem from yesterday’s lesson.)

         The kids get to use their notes and math encyclopedias on the routines, and we go over the results really quickly.  The whole thing takes about 15 minutes each day. 

         • The second benefit of a daily routine is that they give you a snapshot of each student at that moment.  This is particularly helpful as you plan your instruction.  I can tell at a glance how many of the kids in my class have mastered yesterday’s lesson or skill, and what the next steps might be.  Because I make my kids show their work on each routine, I can pinpoint where in the process of problem-solving they are struggling. 

          • Finally they give kids a terrific sense of competence.  As they experience over a series of weeks and months the increasing ease of solving problems using skills they’ve learned, they realize that they can do it, that they are actually good at it. 

         The other day, a parent of one of my general education math students told me that her daughter, who has always struggled with math, is coming home saying “hey, mom!  I’m smart at math!”  This student is the first to raise her hand in my class, the first to want to show the class how she solved a problem, the first to ask questions, and the first to finish her work these days.  It’s not because of me; it’s because every day, when she starts learning math, she is reminded that she’s already got terrific skills.

          Many special educators neglect daily routines, or don’t make their routines as comprehensive as they should be.  We need to recognize that our kids should have multiple opportunities, over a long period of time, to practice newly-mastered skills, or those skills will evaporate like steam after a shower. 

          We need to challenge our kids daily, while at the same time reminding them that they have ability already, or they will never challenge themselves, and never remind themselves of how far they’ve come.

          We need to push, push, push our kids, using all of their strengths, innate and learned, or they will never catch up to their general education peers. 

          In a demanding classroom, mastery is not something to be admired and then ignored; it’s about skill sets we use, reuse, and apply in newer ways on a regular basis.

         There has long been a debate about the issue of teaching to mastery.  When districts and states set up learning modules on a schedule, or a series of standards to meet each year, the inclination of many teachers is to get through as many of them as possible. Some schools and districts place a great deal of pressure on teachers to move forward, and to keep moving through the year.

         I’m not averse to having a set of outcomes to work toward and achieve each year for each grade level. I am against moving forward before our kids really have become proficient at new skills, strategies, and knowledge.

         In a demanding classroom, we don’t get stuck in a routine of doing the same work over and over, and we don’t adhere to other people’s schedules about when learning should be accomplished. Instead, we focus on cementing new skills, step-by-step, concept-by-concept, so that when the foundation of math, science, and other learning is complete, there are as few weak spots as possible.

         If you think about it, if we move kids forward before they really get the previous unit or skill, you are building a house of cards on quicksand. Nothing is going to really stick and the child is going to be aware on a pretty consistent basis that he or she is missing something.

         And what are we teaching kids about learning if we do it this way? It seems to me that we are saying to our children: Learning isn’t about mastering information and strategies; it’s about zipping through lessons to completion rather than to skill.

         Given that one of the major issues for kids with special needs is that they rush through work, getting it done rather than getting it right, aren’t we re-enforcing their own poor learning habits when we teach to completion over quality?

         Many will argue that teaching to mastery takes too much time, and that we don’t have the extra hours or days to ensure that all of our students become proficient at each new lesson.

         I disagree. It isn’t necessarily so. It all depends on how we teach the new information or skills, and what kind and what quality of practice we give our students.

         It also depends on the manner in which we release responsibility back to kids as they work. If we jump too quickly from “I show you” to “you do it,” mastery will take much longer than if we move, increment by increment, from “I show you,” to “I show you again,” to “we do it together,” to “we do it together more,” to “you and a partner do it,, to “try it again, and I’ll be right here,” to “hey, try it and I’ll step back a bit,” to “hey, you can do this!”

         All of that, by the way, doesn’t take place in math, for example, for weeks and weeks; it’s really a matter of days.