The mastery of basic facts is critical if students are to develop fluency in working mathematical problems. The negative attitudes many children have about math can be traced to not having mastered the basic facts.[1]

Yes, I admit it – I think kids should have to learn math facts – yes!  I know it’s boring.  I know it’s painful, but it’s not as painful as sitting in a grade 9 math class not being able to factor a binomial or polynomial because you never learned the relationship among the numbers 8, 7, and 56.   

When I ran a school for students with special needs in Richmond Hill, I taught mental math for a full month before we cracked a text or looked at problem solving.  My grade 6 to 9 students learned math facts to 12 x 12, and then they learned how to solve computational problems, such as 15 x 28 or 165 x 23, in their heads. 

And they loved it. Why?  Because they could do it – and it made them feel good (their peers in the public and private systems couldn’t do it) – and when we did get to the various curricula, they weren’t sweating the small stuff. 

And they weren’t using calculators. 

TIPS for teaching multiplication facts to 12 x 12:

ü  Spend 7 minutes a day.  Every day.  Okay, every weekday.

ü  Work with only 2 new facts at a time.  Add them to the existing deck, so your child is reviewing every single day.

ü  Once you teach a multiplication fact, e.g., 7 x 8 = 56, teach its turn-around fact, 8 x 7 = 56 (just because it’s obvious to you doesn’t mean your child will see it).

ü  Teach division facts at the same time, with their turn-arounds (56 : 8 = 7 and 56 : 7 =8).

ü  Put the focus on accuracy first; then worry about speed.

ü  Try this order (and feel free to build a reward system into this programme).

•  x 0 and x 1 = you can knock these off in a few minutes with most kids.   
• x 2
• x 10
• x 5
• x 9
• x 11
• squares (2 x 2; 3 x 3,  etc.)
• Then the rest, starting with 3 x ……. Don’t become discouraged. Picture a 12 x 12 grid.   If you wrote the answers to all those multiplication and division facts you’ve just learned into a multiplication grid, you’d see, there aren’t many left to learn!

Don’t stop reviewing just because your child knows the facts this week.  Keep it up a few times a week for 5 minutes.  

Before you protest… I agree.  Some children with learning disabilities have to expend too much energy to learn math facts, especially those with dyslexia and memory deficits.  For those students, I suggest, not calculators, but fact sheets for addition, subtraction, multiplication, and division. Feel free to contact me if you’d like a sample of our math fact sheets.

Until next time,

Diane 

---

[1] Mattingly, J. C. & Bott, D. A. (1990).  Teaching multiplication facts to students with learning problems.  Exceptional Children 56, p. 44.

THE CREATION OF THE TEACHER
  – Author Unknown 

The gods were designing teachers.

Even though it was their sixth day of overtime on this project, the gods didn’t mind.  They knew this design was critical.  Teachers would touch the lives of so many.

An acolyte appeared. “You’re sure taking a long time to figure this one out.”

“We know,” said the gods, “but have you read the specs on this order?”

Teacher Specifications:…must stand above all students, yet be on their level … must be able to do 180 things not connected with the subject being taught … must run on coffee and leftovers, … must communicate vital knowledge to all students daily and be right most of the time … must have more time for others than for herself/himself … must have a smile that can endure through pay cuts, problematic children, and worried parents … must go on teaching when parents question every move and others are not supportive … must have 6 pair of hands.

 

“Six pair of hands,” said the acolyte. “That’s impossible.”

“Well,” said the gods,” it’s not really the hands that are the problem.  It’s the three pairs of eyes that we’re having trouble with!”

The acolyte looked incredulous.  ”Three pairs of eyes?  On a standard model?”

One of the gods nodded and explained.  ”One pair of eyes to see a student for what she is and not what the way others have labelled her.  A second pair goes in the back of the teacher’s head to see what should not be seen, but what must be known.  But it’s the third set that’s really tough,” said the god.

“Tougher than eyes in the front and the back of the head?” the acolyte asked.

“Yes,” said the god. “The third pair is truly special.  Even when a child misbehaves, these eyes see only the goodness in the child – and they manage to send the child a message of understanding and acceptance without the teacher saying a word.”

“Wow,” said the acolyte. “This is a huge project.  Maybe you should take a break.”

“We can’t,” said one of the gods.  “We’re close to creating something much like ourselves. 

“Yeah,” joined in another one of the gods.  “We have one that comes to work when he/she is sick…..teaches children who don’t want to learn….has a special place in his/her heart for children who aren’t his/her own…..understands the struggles of those who have difficulty….never takes the students for granted…”

The acolyte looked closely at the model the gods were creating.  ”Sounds a little soft-hearted.”

“Yes, it’s soft-hearted,” said one of the gods, “but it’s also tough.  You can’t imagine what this teacher can do – or ensure – if necessary”.

“Can it think for itself?” asked the acolyte.

“Not only think,” said the god, “but also reason and compromise with adults and children.”

The acolyte moved closer to get a better look and ran his finger over the teacher’s cheek.

“Well,” said the acolyte.  “I think you do need to take a break.  This one has a flaw.  It’s leaking.”

The gods moved in closer and one of them lifted the drop of moisture from the teacher’s cheek.  “Hmm,” she said, “it’s a tear – not a leak.”

“A tear?  asked the acolyte. “Why a tear?”

The gods conferred for a few minutes. Then one of them replied. “The tear is for the joy and pride of seeing a child accomplish even the smallest task.   It’s for the loneliness of children who have a hard time fitting in.  It’s for the anguish of those children’s parents.  It’s for the pain of not being able to reach some children and for the shame those children will feel in themselves.  It’s for every goodbye at the end of the year.”

“My, “said the acolyte,” The tear thing is a great idea…You gods really are geniuses!”

The gods looked at each other, and then back at the acolyte, shaking their heads as one.  “We can’t take credit.  We didn’t put it there.”

“The Creation of the Teacher“ was found at http://www.dltk-kids.com/school/poems_for_teachers.htm – and edited by D. Duff

Just came in from a home visit with a client family.  The parents of a nine year old have decided their son doesn’t need to learn math facts – neither addition, subtraction, multiplication or addition.

I’m going to blog about rote learning (and about Daniel Willingham’s take on it in “Why don’t students like school?) in a few weeks, but I thought I’d  like to get the debate started. 

How do you feel about children having to learn times tables and addition/subtraction facts?

Do you think the school should ensure kids learn these facts?  Do you think it should be up to parents?  Do you think it’s a waste of time or a necessarily bundle of knowledge?

Please share your perspective in the comments section below (and don’t forget to tell us if you are a parent or an educator), and then accept our little bit of fun in return:  Ma and Pa Kettle – and the New Math.

I was going to write about chapter 4 of Willingham’s Why Don’t Students Like School? and was really looking forward to it because it deals with rote learning (a debate in which I often find myself alone on the pro-team).

But rote learning is going to have to wait while I rant a bit about another subject that riles people’s tempers – homework.

Homework of questionable value, to be specific.

I was at the home of a very bright grade 4 student a couple of weeks ago.

In the living room, I saw pieces of bristol board, cut and glued into turrets (yes, as in castle); popsicle stick draw bridge and portcullis (a term I’ve never heard in 52+ year.  And, I might add, I’ve managed to be a fully functioning adult professional anyway.  For those of you who do  fear the shame of not knowing what a portcullis is, please refer to this fun site:  http://www.castles-of-britain.com/castlesn.htm).

In the kitchen were bits of paper, keepers and discards of various sizes and shapes.  The larger pieces – the keepers with designs which looked like bricks – had been carefully coloured a variety of shades of brown/grey.  The smaller pieces – the discards – were being swept into a dustpan with a dry rag.  The hand on the rag belonged to the frazzled father.

“I don’t know what the point of this is,“ he said, in a tone that mirrored his words.  “It’s taking all three of us to get it done.”    

I asked how much time they’d put into it already. 

12 hours.  

Now, I know the student had been working on this project for quite a while, because I visit twice and week, and I’ve seen it progress over several visits.  Progress and grow into something the dad had begun to resent.

My student became distressed when she heard her dad tell me the assignment was due in four days: “I still have to put it together, and make the moat, and the stables, and the kitchen, and where people sleep,” she moaned. 

“Don’t worry,” the dad said.  “It will be done.  That’s why mom and I are helping you.”

Dad looked at me.  “I’d like to just sweep the whole thing into a box as it is and carry it in to the teacher,” he said. “We’ve got a neighbour whose child has a similar project – also not very impressed.”

I was out to see the student again this week and this time it was the mom who was home.  Shaking her head, she showed me the pictures she had posted on Facebook for friends and family. 

I asked what they’d do with the project when it was time to bring it home. 

“Wrap it up and put it in the basement,” she said, “in case her brother has to do it when he gets to grade 4.”

Did she ever question the pedagogical value, I wondered.  (She’s an assistant at a Montessori school.)

“No.  I figure if we ever go back to the dark ages, she’ll know how to build her own home.”

Well, the mom might have had a sense of humour.  But, I was with the dad on this one.  What was the point, academically speaking? 

I can’t help but think that an entire classroom of students could have researched, planned, designed and constructed a castle in a few social studies periods – with lots of valuable learning about collaboration, time management, negotiation, and peer-teaching to be had.  In addition to learning what a portcullis is.

How would YOU vote on this one?  Would you share the laugh with Mom – or join Dad in his frustration about this kind of assignment?  Weigh in and let us know, won’t you?

Diane Duff, B. Ed., M. A., has been working with students and families for almost twenty years.   Her areas of expertise are literacy development, special education, reading disability/dyslexia, and teacher training.   At Aldridge-Duff, the private education business she founded ten years ago, Diane coordinates a highly experienced team of certified teachers  who provide in-home tutoring and academic support to students (all ages/grades/abilities) in both Ottawa and Toronto.

 

Contact Diane directly at aldridge@bellnet.ca 

www.aldridgeduff.ca

*photo courtesy of Flickr

 

….. a pause in the book review

I was happy to receive an email from a reader of this blog – and doubly so because the question touched on one of the subjects dearest to my heart: students with learning disabilities.

“Hi Diane. I teach grade 10 history and English in a school that isn’t exactly overflowing with resources. Lots of my students have trouble reading at grade level and a couple have attention deficit and don’t focus well so I worry about whether they can really get the information from the textbook that I want them to. Do you have any suggestions? Thanks. Leslie S.”

Hi, Leslie. Given your comment about resources, I’m going to assume you don’t have access to special education personnel or a teacher’s aide. That means there’s a lot of pressure on you to help students with a variety of learning needs wade through the same learning materials.

There are ways to modify textbooks, such as highlighting important sections, reading them onto tape that students can listen to (especially effective if the sections are also previewed and summarized on tape), or finding high-interest, low vocabulary alternatives. These are all effective, but not always practical. Highlighting textbooks doesn’t help those who cannot read, but may help focus the attention of those who get lost in details and can’t differentiate the important from the insignificant. Taping the texts (and providing summaries) is time consuming in the extreme, and high-interest, low vocabulary alternatives, when available, don’t always cover all the same content as your textbook.

My first suggestion would be not to rely exclusively on a single publisher’s text. Use a variety of materials, from novels on tape and DVDs to help teach narrative structure, to poetry, newspaper articles (archives), letters, textbooks, poetry, websites to provide students access to history.

But, when the textbook is where you need the students to focus, try these suggestions:

1. Teach students how textbooks work by helping them understand that each chapter of a single text will be laid out much the same way, and that much can be learned from

a. Introduction/preview

b. Headings/subheadings

c. Summary

d. End of chapter questions

In fact, I always ask students to read the chapter summary first. Then I want them to read the questions and discuss, as a group, which ones they think they know something about, and which ones are completely foreign. In this way they are activating their background knowledge – and, with any luck, developing an interest in the topic.

2. Preview each section for your students. Look over the headings and subheadings. Talk about what will likely be discussed. Then give them a short summary of the section before assigning the actual reading. Provide a few questions to be answered from each section and subsection to keep them on track.

3. Pre-teach important vocabulary and concepts and provide written notes after these mini-lessons.

4. Provide your students with advance organizers such as an outline of vital information or a graphic which shows them super-ordinate and subordinate information. You can even write page numbers on your outline or graphic to help students find the details they need in the text.

5. Ask students to generate a list of questions after they attend your vocabulary/concepts mini lessons and review your advance organizer.

One of my favourite books in teacher’s college and in my early years of teaching was Content Area Reading (Third Edition) by Vacca and Vacca. The authors divided the book into three sections: Establishing a Context for Instruction, Reading, Writing, and Study Strategies, and Translating Knowledge into Practice.

The teacher-friendly text has maintained its popularity and usefulness and is now in its 8th edition, with revised chapter on “Struggling Readers and Writers,” and new chapters “Linguistic and Cultural Diversity” and “Learning with Electronic Texts.”

If you’re not signed up for a summer course when school breaks in June, Leslie, maybe some reading about how to help students read texts could be a part of your summer professional development plan.

Content Area Reading: Literacy and Learning Across the Curriculum (8th Edition)

Thanks for the question, Leslie. Hope this helped.

See you in a couple of weeks, folks.

Diane

……. a pause in the book review

To be a Substitute (Occasional) Teacher

In hiring professionals to work as in-home tutors, I meet a lot of new teachers, and a lot of new-to-Canada teachers.

While they wait for the chance to prove themselves in permanent teaching positions, many spend their evenings and weekends working as teacher-tutors – happy to be working in their field.  By day, they want the chance to gain experience and make connections by filling in when their fully-employed peers have to be away from the classroom.  They want work as occasional teachers.

But not all can afford to wait for occasional work, to keep their weekday schedules free so they are available to teach on an hour’s notice.  Too many are under-employed at jobs that allow them to feed their families, but restrict their chances of realizing employment in their chosen profession.

In these ways, the experiences of new teachers and new-to-Canada teachers are the same.  But, new-to-Canada teachers may have more difficulty, not only securing that ever-elusive full time teaching job, but also securing occasional teaching work.

The experiences of three new-to-Canada teachers, Sonia, Zahra and Ogus, are given voice in Katina Pollock’s “Marginalization and the Occasional Teacher Workforce in Ontario: The Case of Internationally Educated Teachers (Canadian Journal of Educational Administration and Policy). http://www.umanitoba.ca/publications/cjeap/articles/pollock-iet.html

Enjoy the read – and please leave a comment.

…..I’ll be back with chapter 4 of Daniel Willingham’s “Why Don’t Students Like School?” in two weeks.

Summary Review of Chapter 3: “Why do students remember everything that’s on television and forget everything I say?”

While driving to see a client this week, I heard a piece on CBC about people forgetting how to read analog clocks because they are surrounded by digital clocks and don’t get a lot of practice with analog. Intrigued, I started to consider my own difficulty remembering which button is which on the remote control. A few minutes later, distracted by traffic, I put the question out of my mind.

But I thought about it again the next day when reading chapter 3 of Willingham’s book about why students don’t like school.

In this chapter, Willingham managed to startle me with the clarity of his definition of memory as “the residue of thought.”

So why is thinking about memory in that way important for teachers? It’s because if we want our students to remember what we teach, we have to construct lessons in such a way as to make them memorable. We have to make them think about what we’re teaching.

We all do that, don’t we, devise creative ways to engage our students?

Willingham provides a great anecdote of a fourth grade teacher who went all out to make sure her young students connected with her lesson about the Underground Railroad. Because biscuits had been a staple food of slaves, the teacher supplied her students with flour and water and all the rest so they could make biscuits themselves.

You know those kids remembered that lesson!

Well, in truth, Willingham says, what those students remembered was not the lesson content – life during the time of the Underground Railroad. No, what they remembered was how to make biscuits – because that’s what they were focussed on. That’s what they were thinking about.

Of course. Of course.

Obviously, there’s more to chapter three than that. Willingham talks about how to construct lessons around narrative structure and he makes a pretty good case that it doesn’t matter what subject we teach. We can use the four Cs of story – causality, conflict, complications and character – to script any lesson.

Interesting stuff. But, frankly, since I swallowed Willingham’s pearl about the difference between memorable and engaging lessons, I’ve been busy revisiting and reconstructing lessons according to what I should have focussed student attention on. So that’s the section of the chapter I remember best.

And, that just makes his point, doesn’t it?

Chapter 3 recommendation: D. L. Schacter’s “The seven sins of memory: How the mind forgets and remembers”

In two weeks: Chapter 4 – Why is it so hard for students to understand abstract ideas?

See you then!

Diane

Summary Review of Chapter 2 – How can I teach students the skills they need when standardized tests require only facts?

When you set out to debunk a statement made not only by a dead man, but by arguably the smartest man ever to have lived, you certainly get your reader’s attention. In chapter 2, Willingham argues that Einstein was wrong when he said, “Imagination is more important than knowledge.”

Willingham thinks that knowledge is pretty darned important – and that we should not abandon the teaching of knowledge in our zeal to teach skills such as critical thinking. In fact, he says we can’t teach critical thinking without teaching facts – because students need to have something to think about.

I’m not sure many would argue with him about this. I don’t think I’ve heard even the staunchest education reformer say we should stop teaching students about things; I seem to recall, rather, that words like meaningless, decontexutalized, and rote were peppered in statements decrying the teaching of facts in isolation.

Willingham spends a lot of time explaining the relationship between factual knowledge and the ability to think critically – a little too many words for my needs or taste, but he does eventually move on to the subject near and dear to my heart – reading.

In this section, Willingham argues that knowledge is essential to reading comprehension – and by knowledge he means background knowledge. He says that we need background knowledge in order to make connections between and among ideas. To do that well, he argues, we must be able to chunk information. Why? Because to think we need to recall information from long term memory and place it into working memory, and we can only hold about seven packages of information in working memory. So, the better we can chunk information into packages, the more we can hold in working memory and bring to bear in critical thinking. The more background knowledge we have, according to Willingham, the better we are at chunking.

Willingham says children as young as preschool need factual information in order to read better, and he refers to the well known study by Chall and Jacobs about the decline in reading scores at grade 4 when more emphasis is put on comprehension skills than decoding skills. Further, he writes about the importance of early acquisition of knowledge and alludes to Stanovich’s “Mathew Effect” when he talks about how those rich with knowledge get richer because they can remember more (they have a frame of reference upon which to hang new information).

So, I was surprised when I got to the section about implications for the classroom. Instead of addressing what the very young ought to be reading and learning – in order to lay the foundation for reading comprehension and for a richer knowledge life – Willingham provides a recommendation suitable for senior students: a daily newspaper and books written for the intelligent laymen. And what books are those? The canon of science and politics written by dead white men. Willingham says that as long as society relies on these texts, these are the ones we need to teach our students. (That statement should provoke a chapter of debate, in a whole different sort of text, methinks.)

Perhaps Willingham was too busy thinking critically about thinking to think imaginatively about how to fill our students with information. From my perspective (without thinking very hard – or very critically- or even very imaginatively), here are a few places to begin:

• expose students as young as SK to as much non-fiction reading as story reading

• preview vocabulary and concepts in non-fiction reading

• include a course in how to teach content area reading in all pre-service training

• teach students content-area reading skills from grade 4 on

Why not leave a comment with your suggestions?

Chapter 2 article recommendations:

1. Chall and Jacob’s “Poor Children’s fourth-grade slump” (originally published in American Educator, 2003) available at http://www.colorincolorado.org/article/13995

2. Stanovich and Cunninghams’ “Where does knowledge come from? Specific associations between print exposure and information acquisition” (originally published in Journal of Educational Psychology, Volume 85) available at http://gse.berkeley.edu/faculty/aecunningham/Wheredoesknowledgecomefrom_Specificassociationsbetweenprintexposureandinformationacquisition.pdf

In two weeks: Chapter 3 – Why do students remember everything that’s on television and forget everything I say?

See you then!

Diane

Summary Review of Chapter 1

Two weeks ago, when I announced my plan to summarize/review this book one chapter at a time, I invited other teachers to read along with me. But, I know that teachers facing a new semester may feel too overwhelmed to read a non-fiction book. That’s okay. Willingham’s first chapter content is – in many ways – second nature to those who spend their lives in the classroom.

The most startling – and counter-intuitive – thing Willingham says is that the brain is not designed for thinking. Well, actually what he says is that the brain is not very good at thinking (no surprise to some teachers) – and that we – and our students – rely on our memory of processes and procedures to help us with a lot of our thinking.

What I appreciated most about chapter 1 was Willingham’s suggestion that teachers keep a diary. This was a valuable reminder to pick up a habit I’ve abandoned. He’s correct – it doesn’t matter how brilliantly (or how poorly) a lesson went – I really don’t remember it a year later – not in detail.

However, the balance of the chapter amounts to a review of pre-service or in-service workshops about planning for meaningful instruction. In short, many teachers will find it to be statements of the obvious:

1. To prevent student boredom, give them something to think about. In Willingham’s view, that means giving students problems to solve. He states what we’ve known for a long time – that instead of dumping facts into the student brain, we need to ignite cognitive energy with the fuel of exciting ideas and then set it to work.

2. Determine that students have the necessary background knowledge to solve the problem – and make sure that the problem is neither too difficult nor too easy.

3. Avoid placing too heavy a cognitive load on students through multi-step instructions or a series of unrelated facts. Slow the pace of the problem pitch and use memory aids so as not to overly tax working memory. Change the pace (shift gears) to get and keep student attention.

4. Accept and act on a variety of student preparation. And, make the problem interesting and relevant.

We all know the importance of making work meaningful, but given the way classrooms are traditionally arranged and managed, it can be challenging for teachers to ignite the curiosity of an entire class. Students don’t walk in the door as a homogeneous group with the same intellectual capacity, the same curiosity, the same content interests or background, or the same motivation.

Willingham suggests grouping students to deal with this challenge. This suggestion is valid in theory, and some of us have used it to advantage is sympathetic teaching environments. But for some, relegating students to small groups doesn’t accomplish what it purports because it is, essentially, an effort to make a systemic change within a rather intractable system.

We may group students according to ability and interest, or even according to their social-emotional needs, but while the educational system holds that they be cast in grade levels and taught the same content, we are still left clutching at the minutes on the clock, trying to stretch time so we can differentiate for all.

If only it were as simple as the TV shows – when the villains waited calmly in the sidelines while the hero dealt with them, one by one.

Chapter 1 book recommendation: Steven Pinker’s “How the Mind Works” (a fun read!)

In two weeks: Chapter 2 – How can I teach students the skills they need when standardized tests require only facts?

See you then!

Diane

I stumbled across the name of Daniel Willingham the other day.  He’s a cognitive psychologist and supporter of the idea that kids will become better readers if they learn more about the world through increased curricular focus on science and social studies.  That idea caught my attention, especially given Ontario’s plans to revisit curriculum – again.  A quick Google search and soon I was listening to a recorded radio interview and nodding my head to his brief comments about:

• • the importance of content knowledge in the ability to read
  • the challenge teachers face in trying to figure out where to “pitch” a concept to a group of students who have different abilities and background knowledge
  • the excessive load that’s placed on the educational system by kids who come from homes that don’t value education
  • the necessity of practice and the importance of rote knowledge in some areas (e.g., math facts)
  • the use of mentorship programmes for new teachers to improve both new teacher retention rates and the quality of their instruction

When I learned Willingham had written Why don’t students like school: A cognitive scientist answers questions about how the mind works and what it means for the classroom, I decided it was a must read.  After all, we all like to spend time with people who think like we do, right?

Have a look at the chapter titles and see if the Willingham’s book doesn’t promise to be delicious.

1)    Why don’t students like school?

2)    How can I teach students the skills they need when standardized tests require only facts?

3)    Why do students remember everything that’s on television and forget everything I say?

4)    Why is it so hard for students to understand abstract ideas?

5)    Is drilling worth it? (Well I’ve already given away the easy answer – but let’s find out what he says about why – it IS a 16 page chapter.)

6)    What’s the secret to getting students to think like real scientists, mathematicians, and historians?

7)    How should I adjust my teaching for different types of learners (Given the current climate of debunking the idea of learning styles, I’m really interested in what he writes in this chapter.)

8)    How can I help slow learners (Is that term politically correct?)

9)    …last chapter is called “What about my mind?” (It’s anyone’s guess what will be in that chapter. Does Willingham discuss how the mind works generally, or how a teacher’s mind ought to work – what knowledge it should contain and what the optimal processing speed is for teaching…)

Intrigued?  I am, especially because I think it’s a pretty safe bet that the book isn’t preachy.  One of the cool things Willingham said in the interview was that researchers shouldn’t boss teachers around (okay, he didn’t use those words exactly). He says he knows the lab, but not the classroom.  No one, he says, knows the classroom better than teachers.  Now, doesn’t he sound like a very smart and cool man?

I’ve ordered the book (Chapters/Indigo and Amazon both carry the hardcover edition) and I’m wondering if any other teachers out there want to order it too – and read along with me.

I thought we could look at a chapter a week and talk about it. I’ll come back here on January 28^th with my reaction to chapter one – “Why don’t students like school?” – and my hope that you’ll have read that chapter too and be ready to post a supportive comment or rebuttal.

Regards,

Diane