* Blogging A-Z wrap up and more

checkered-flags-309794_640Thanks to Nerd in the Brain, I discovered that I should leave some feedback on April’s Blogging A-Z challenge.  I loved every post of it, probably because I was in one of my favorite modes: catch up!  I started late and enjoyed the challenge of catching up and even finishing a day early.

The challenge of catching up is one reason I love special education.  It’s a challenge worth taking.  This summer I face two major challenges: bringing two students to grade level and beyond, one in reading and one in math.  Both are twice exceptional students.  Both have known more than their share of heartache and failure.  These kids and their families are committed and motivated to the task that lies ahead.  It’s a daunting one, in many ways, but I am confident that together, we can finish well.

I will share my experiences as we use this summer “break” to reach a knowledge-appropriate finish line, with renewed confidence for the upcoming school year.

* Math Struggles 301: Effective strategies

Sousa mathIn David Sousa’s book “How The Brain Learns Mathematics,” he cites researchers who have found that number sense is not intrinsic but can be shaped though both formal and informal activities.  Sousa lists a number of effective strategies for developing number sense.  Here are a few of them:

Meaningful estimates.  Helping students practice meaningful estimates goes far beyond, “Guess how many goldfish crackers are in the jar.”  In my experience, those kinds of estimates require more than number sense; they tap visual spatial understandings, as well.  Estimation jars are often used in lower grades where many kids are unlikely to have sufficient practice with this skill.  Early number estimates should involve items and quantities which can easily be counted (certainly less than a hundred) so that kids can improve their ability to estimate.  Kids should also be exposed to multiple opportunities for making reasonable estimates. Teachers can create realistic and necessary opportunities for estimation.  For instance, kids might estimate how many books are in a reading bin and how many pencils are in a caddy.  It’s important for kids to learn early on that estimation is not just another tedious step on worksheets, that estimation is not a hurdle to make math more burdensome.  One student recently blew off the estimation portion of his classroom assignment, saying, “It doesn’t matter what I get.  Anything is right.”  Clearly, estimation was taught in isolation and as a meaningless activity.

Solve problems and consider the reasonableness of the solutions.  This strategy sounds reasonable, but for kids with math difficulties, an unreasonable answer can be hard to recognize.  The kind of problem where I typically see younger kids struggling is comparing values or quantities.  A classic question is: If Kevin is 8 and his sister is 5, how much older is Kevin?  The majority of K-2 special needs kids I teach will add those two numbers and feel their answer is reasonable.  They have learned to subtract when items are missing, eaten, or given away, but using subtraction to compare is another beast altogether.  Some kids learn faster when they start solving this type of problem with pieces of cereal or other food.  Using cubes that interlock or stacking blocks is another way to visualize the number comparison problem, helping them “see” how much more one quantity is than another.  It can take a LOT of experience for kids with math difficulties to master this process.  Simply asking students if their answer is reasonable is ineffective if not preceded by plenty of experience with manipulatives and real-life math problems.

Model the enjoyment of numbers and number patterns.  Research studies conclude that the teacher’s attitude “is the most critical factor in establishing a climate for curiosity and enjoyment of mathematics.”  For me personally, this statement means that I must watch myself for subtle (and not-so-subtle) signs that math has not been my favorite subject.  As I set a goal of making math enjoyable for my students, I am also enjoying it more.  I ask myself: If I am short on time, what subject is going to be curtailed?  Do I look for opportunities to create and solve math problems?  Do I encourage kids to talk to each other during math instruction?  Is my math instruction engaging and meaningful?  Integrating math into other content areas is a terrific way to make problem solving meaningful.  Free Math is another classroom strategy to provide time and resources for those “random” math questions that arise during the course of the day.  Dedicate a space where teacher and kids can jot/dictate questions on sticky notes, to be addressed during Free Math time.

Do you have favorite strategies for developing number sense?

* Teaching: tyranny of the urgent

Alarm-Clock-Simple--4926-largeTutoring students in a one-to-one setting without typical classroom constraints has its advantages.  I enjoy being able to select appropriate materials, tailor activities to student interests, and address skills without the pressure of teaching the core curriculum.  On the other hand, I am frequently in the same battle as resource teachers and other specialists.  Homework and projects routinely impact my valuable time with students.  You know that I am not keen on homework, if you’ve been following this blog.  After an hour or more of tutoring, I don’t want my students to face a stack of homework, so I typically assist them to complete it as quickly as possible during our session.  But the disconnect between students’ skills and their homework drives me NUTS!

Here’s what happened today:  I was teaching a fourth grader who is struggling with math.  I wanted to continue our work on place value and rounding numbers.  Instead, I checked his homework and took a deep breath.  It was algebra (or “algebraic,” as he told me).  Knowing that he works much better on frustrating tasks with me than his parents (it was that way with my own kiddos), I decided to bite the bullet.  Here is a sample problem:  Sue had 5 times more pencils than Nate.  Together they had 18 pencils.  How many pencils does Sue have?  How many more pencils does she have than Nate?  My student was required to model the problem using symbols and write three or four equations to demonstrate how he solved it.

I imagine some kids in his class are totally ready for that problem.  But my student was not.  He had no idea where to start, was dealing with abstract procedures that made no sense to him, and didn’t have sufficient opportunities to work with manipulatives (and perhaps understand) what “5 times more” actually means.  This is a student who does not know when to add or subtract.  Not only did we lose valuable instructional time on the skills which match his current math understandings, but he needed two brain breaks in order to survive that portion of our session.  And what does he know after our “guided practice?”  Not a lot.

I was facing the dilemma described in an interesting article called “The Hard Part” (thank you, Tony’s mom!).  In his column in the Huffington Post, Peter Greene writes about teaching: “The hard part of teaching is coming to grips with this:  There is never enough.  There is never enough time. There are never enough resources. There is never enough you.”  Indeed!

I do understand that the classroom teacher has her own constraints.  She is required to teach “algebraic” for a short period of time and then assess, assess, and reassess.  How can she “individualize” the above assignment for my student when it is totally inappropriate for his current level of functioning?  He needs more opportunities to model multiplication, much less solving problems with variables.  His dilemma reminds me of my post from yesterday on “How The Brain Learns Mathematics” by David Sousa.  Sousa describes prerequisite skills for learning mathematics successfully, including the ability to visualize and manipulate mental pictures and the ability to reason deductively and inductively.  My 4th grader is particularly weak in those skills.  When will he have time to catch up?  Isn’t that what summers are for?

* Math Struggles 201: Brain-based teaching

Sousa mathI am enjoying another Corwin Press book on brain-based teaching: How The Brain Learns Mathematics.  In David Sousa’s chapter on identifying math difficulties, he first suggests that teachers analyze the type of math instruction being provided and consider other environmental issues before determining that a child has an actual disability.  He describes some of the pitfalls of current math instruction.  Sousa’s book provides excellent strategies to support students at different developmental levels. It also describes effective assessment for determining a student’s present level of performance.

Sousa reviews research that describes a continuum of learning preferences for quantitative versus qualitative reasoning.  Some mathematical behaviors associated with quantitative reasoning include a proclivity for linear thinking, an emphasis upon the components of problems rather than broader concepts, and difficulty with multi-step problems.  Qualitative reasoning is characterized by emphasis upon broader concepts, difficulties with precise calculations, multiple approaches to problem solving, and an enjoyment of geometry.

From Sousa’s description of this continuum, I immediately thought of dyslexic readers, who often have a better grasp of the “gestalt” and experience more difficulty with the “smaller” components of language.  However, Sousa cites research indicating that dyscalculia and dyslexia are not genetically linked, although kids may certainly have both impairments.

Research supports the use of a concrete-pictorial-abstract approach to math instruction, which allows students at all levels (including middle and high school) the opportunity to interact with math via manipulatives first.  (Check out Nerd in the Brain‘s website for her awesome use of math manipulatives.)  During the concrete stage, it is important to link math to real-world problems.  Students then transition to pictures which assist students in visualizing the math process.  The last step is the use of symbols as a more efficient means of representing mathematical operations.  Sousa emphasizes that without a concrete link between symbols and real-world problems, students will simply memorize material and procedures without understanding.

Depending upon the current bandwagon, I’ve seen math instruction stall at the concrete level or actually start at the symbolic level.  Over the years, regular classroom math instruction most often whisks students into the symbolic level too quickly.  I have also been guilty of rushing students through the concrete level because they may “waste time” or become distracted by playing with materials.  It’s a challenge to make math instruction efficient as well as cognitively appropriate.  I have found that an effective assessment eliminates some of that pressure because I can better target my instruction.  For kids who absolutely cannot touch manipulatives without building towers, there are some good online manipulatives which allow them to experiment without getting mentally lost.  Glencoe has a super set of free manipulatives, with creative work mats that kids truly enjoy.  The National Library of Virtual Manipulatives is also excellent (and free) but doesn’t have the flexibility of Glencoe’s site for creating real-world problems.

* Math: homeschooling kids with attention problems

how-to-improve-concentration-01In response to a question, here are some strategies I have found effective when teaching math to kids with attention problems.

1.  Make sure you complete adequate assessment so you have a solid idea of where to start instruction.  The National Council of Teachers of Mathematics offers an effective overview of the basic strands of mathematics instruction for all grade levels: numbers and operations, algebra (don’t panic- this includes sorting, classification, and patterns at lower grade levels), geometry, measurement, and data analysis and probability.  They also emphasize the importance of problem solving and reasoning.

2.  Make the content meaningful.  If your child has musical interests, create authentic problems related to music.  For instance, you could compare the number of black to white keys on a piano, solve problems related to how many keys are not used when playing a melody, or determine how many two-note chords are played per minute.  Use proper names that trigger some association for your child (such as siblings, parents, and friends).  Make the problems humorous or include a competitive angle, depending upon your child’s characteristics; I find that kids enjoy problems portraying a bit of friendly competition with others.  (If you don’t know how to write effective word problems, use commercially prepared materials and adapt the questions.)   Remember to introduce kids to multi-step problem solving as early as possible.

3.  Make practice meaningful without being deadly.  Start with guided practice until the student demonstrates mastery, then practice over time for long-term retention.  Achieve higher levels of automaticity by using timed fluency of math facts, letting your child fill in graphs of progress.  Have kids complete the smallest number of problems necessary to gain competence and show retention.  Successful focus on 10 problems is far superior to desultory performance on 25 problems.  Avoid cluttered pages.  Avoid pages with so much content that your child is stressed as soon as they see the assignment.

4.  Make sure you include reasoning and interaction as your child works on math.  You could film your child’s explanations while problem solving and watch them as a review of skills, an assessment, or to coach younger siblings.

5.  Make time for breaks.  Home-schooling allows you flexibility in scheduling math when your child is most alert.  You may also provide more frequent breaks (and brain breaks) for a child who is easily fatigued or distracted.  Use a timer so your child can see when breaks will occur.

6.  Make effective use of technology and games.  Use online resources which allow for experimentation and use of manipulatives.  Math Is Fun, National Library of Virtual Manipulatives, and Illuminations are three of my favorites.  Some kids with attention problems may be overly distracted by certain manipulatives, but it is important to find those that work effectively for your child.  Consider creating a digital portfolio for the school year.  Your child can help decide which math work and videos to include (see #4 above).  Check out the websites in my Technology Cools section.

Are these suggestions helpful?  Do you have any other tips for readers?

* Math struggles 101: Overview of problems

math struggles 1There’s not enough time!  No, this post isn’t about learning to tell time.  It’s about helping special needs kids catch up in math.  I have found it far easier to assist kids in “jumping” a couple of years in reading than making equivalent gains in math.  Why is that?  I have blamed myself much of time.  Math is not my favorite subject and I haven’t had as much experience teaching kids with dyscalculia.  Because reading problems affect performance in all other academic areas, I have provided disproportionate help in reading, if both math and reading are delayed.  There is less stigma associated with a math disability than with dyslexia.  And to top it off, approaches to math instruction in classrooms vary widely from district to district and year to year.

Educational specialists face a serious dilemma in helping kids with math disabilities: Every year, more facts and processes are “piled” on top of a shaky foundation.  The kids I’ve supported typically lack the language of math, for starters.  They have to be taught to recognize phrases which imply that quantities are being combined or separated.  These kids also lack number sense; they don’t recognize unlikely or unreasonable answers.  Ask these kids to find a number on a hundreds board and they panic; they don’t see any patterns at all.  They struggle to visualize math problems and number lines.  They never seem to know where to start when faced with problem solving.  These kids typically struggle to memorize math facts.  I’m currently teaching a fourth grader who cannot compute 2 + 3 without using his fingers.

Kids learn best when they can solve problems that are at a “just right” level: not too difficult but not too easy, either.  In my experience, kids are not usually identified with math disabilities until they are already well below grade level expectations. This means they have spent a lot of time frustrated, copying others’ work, and trying desperately to memorize snippets from classroom instruction.  Effective mathematics instruction allows time for kids to reason, to experiment with strategies, and to share that problem-solving experience with others (whether peers or teachers).  When a student needs special education support in math, that time is shortened.  As a specialist, I must now prioritize my instruction.  My students’ peers are racing along the math road and we are crawling behind.  An effective math assessment is a crucial first step.  I must complete an informal assessment and review standardized testing, along with analysis of classroom work samples and teacher evaluations, in order to write an effective IEP.

I will be sharing more about effective strategies for teaching math, including current neuroeducational research that enables teachers like me to use brain-friendly teaching strategies.  Stay tuned!

* Making eight

A great way to consider subtraction, PLUS more super math conversations about math.

Talking Math with Your Kids

I am writing a book. In the process of doing this, I come across homework assignments that parents find frustrating, and that they share on social media. These almost always get me thinking, and they frequently lead to math talks with my children.

This past weekend was one such instance.

Worksheet: "The whole is 8. One part is 8. What is the other part?"

Talking Math with Your Kids is not a place to hash out the details of whether this is a well written question, or whether this was an appropriate homework assignment for this child. We can discuss that on Twitter if you like, or through my About/Contact page.

Talking Math with Your Kids is about taking opportunities to have math conversations with our children. In that spirit, I share the conversation we had in our house.

Out of the blue, I asked Tabitha (7 years old) if I could ask her a math question. It was maybe Saturday afternoon. We had…

View original post 669 more words

* MathCoach Interactive

MathCoach Interactive is an ambitious site with a huge amount of resources for teaching elementary mathematics.  It has two basic paths for students: one is module based (Topic Progressions), which starts with a pre-assessment and allows the program to determine the next steps.  The other path is lesson based (Grade learning Paths), with a program determined by the teacher.  There are excellent teaching videos for most specific skills, along with games that reinforce those skills.  A writing or student feedback feature is also available, where students can describe the strategies they used.  The program is pricey for a classroom teacher but reasonable for homeschooling or tutoring.  The support folks I’ve talked to have been real teachers who understand math instruction.  You must use Firefox, Chrome, or Safari for the program to run properly.  This the screen you see after logging in.

Math Coach interactive

What kids do:  After logging in, students can create an avatar from a variety of cartoon-like characters and animals.  Here’s an example:

math coach for kid

Students can view their most recent assignments and progress at the top of the screen, the completed assignments in the “Done” category (available by date ranges), and their unassigned work/games under “On My Own” at the bottom (again listed by date ranges).  Looking at the left sidebar, you see that students may select their own activities from the same subject menu as teachers and look at/print special certificates on their Brag Page.  When a student completes an assignment, they click “turn it in” and that work cannot be modified by the student again.  Students may also click “back” or home/dashboard” to return without completing an assignment and return to it at a later date.

What teachers get:  As noted above, teachers may work from either or both of two modes: module-based and lesson based.  You may search through a sequence of all math skills for kindergarten through fifth grade, or go to a module on a specific skill.  Under each skill, you will see what resources are available for that skill (whether printable, online, video and/or game) as well as a reference to Common Core State Standards.  Referring to the top illustration, you can see that it’s possible to search for a specific skill or worksheet, as well for as online practice (which includes games and teaching videos).  For any lesson you want to assign, there is a link for “assign,” “play,” or “download,” as appropriate.  Teachers can monitor student progress through their Gradebook.


  • This program provides a complete scope and sequence for teaching math skills at 6 grade levels, which is very impressive.
  • There are an incredible number of printable worksheets available.
  • The teaching videos are excellent, with a real person guiding students through a concept.
  • The games closely match skills being taught and students seem to find them interesting overall.
  • Students may choose how they play many of the games (by selecting variables, type of play, etc.).
  • Monitoring and managing students is quite simple.
  • The Help section is well organized and provides solid support.
  • The graphics and images are excellent.
  • Assigning activities is very simple.


  • The site needs a better linking system (I’m sure there’s a technical term for that- hyperlinks?).  Every link opens a new window, so students (and teachers) may have multiple homepages opened at once.  There will also be a new tab for anything you open, which is equally confusing.  Partial Fix: Keep closing all but one homepage.
  • Printable student assignments can be humongous, which is startling for both teachers and student (see the 64 exercises above).  Printables cannot be monitored by a computer; it is often difficult to enter responses because theses exercises were never intended to be used online.  They are only useful if downloaded and even then, they are often very lengthy.  Fix: Only download printables.
  • If students do not return to their homepage, none of their work is saved.  Fix: Remind them to return to their homepage.
  • If students select “turn in assignment” before it is completed, they cannot do anything about it.  Partial Fix: Remind them to be careful about finishing before turning in work.
  • Student scores are always visible within a specific date range.  For fragile learners, it can be devastating to see a 17% score on an assessment.  Partial Fix: In the case of the above student, I created a new home page so that that child’s previous scores and assignments were no longer visible.
  • Related to the point above, a student can also venture “on their own” and then face an equally dismaying set of scores.  Partial Fix: Over time, those scores will not be evident unless you change the date ranges.
  • Once a student starts an assignment, the teacher cannot delete it, even if it turns out to be a mismatch for that kid.  Partial Fix: Be careful when assigning lessons.
  • Some students want to change their avatar with each log in or open homepage.  Partial Fix: Set a limit on the number of avatar changes per a certain time period.
  • While the videos and lesson introductions use real voices, other content is read by a robotic male.  Fix: Just laugh along with the kids.

Top recommendation to MathCoach: Hire a new programmer to Improve links to eliminate multiple open windows; allow teachers to remove scores and assignments from students’ homepages; make printables downloadable only; and allow teachers to determine whether an avatar may be changed once selected.

My rating: 3 out of 5 stars.