The Rookery

Problem of the Week has been a part of my practice since my student teaching days.  In New York at the time, all students were asked to show the pathway they took to solving a multi-step problem.  They were only given partial credit for a correct numeric answer – the emphasis was on the math logic they used.  It was hard but it got easier with practice and, more importantly, as students gained confidence in explaining their math thinking to others, they came to better understand and trust the math they were doing to solve the problems.  When they had to explain it, they understood it better and could apply it more flexibly in new situations.

We do a lot of explaining of our math thinking during our regular math day* — kids are pushed to share why something works or how they approached a problem.  But it can be hard to hear from every child for every experience we do.  Problem of the Week insures that every child gets a chance to wrestle with the problem and explain the process of solving it.

Many Pathways, Relevant Math – I try to create problems that have different pathways to a solution.  Some of those pathways may be more efficient than others but children should choose the pathway that makes the most sense to them (which will often be the one they can explain most easily.)  The math is sometimes a direct echo of something we've done in class recently but it can also be an engaging situation that's not based on exactly what we're doing in exploration math right now.

"Getting It" is not black and white - Math problem solving involves detective work and puzzling things out.  I emphasize to students that while their first impulse might be to say, "I don't get it," they should try to shift that to "What do I get?"  How far can I act out or draw the problem?  What's in bold?  What are the numbers involved?  What are they counting?  Even taking a deep breath and re-reading (or having someone else read it while you listen) is a great way to figure out more.

Rough vs. Finished work – Some kids like to do a messy page of numbers and doodles and thinking while they are finding an answer.  Then they go back and write more formally on their Problem of the Week.  They need to move through the process before they are able to articulate Step One and Step Two.  It also helps them see when a table might be useful to display patterns or when you did the same thing with a second set of numbers (so you don't have to explain everything over and over again!).  Adding labels to numbers in equations is a sure way to make one's thinking more clear (both to yourself and others.)

How to Help – It is not an expectation that you help with Problem of the Week.  If a child works independently on it for half an hour and can truly not get anything down on the paper they can turn that in (although I would encourage them to at least write down the important numbers.) . But, if you do want to help, it can be an invaluable time for your child to see how to approach a problem.

• Re-read the problem together part by part. 
• Together, draw out what is going on or act it out.
• Ask your child to highlight the numbers in the problem (including what the numbers are counting)
• Ask your child what they are trying to figure out (it's the bold part of the problem).  What would they need to know to figure that out?
• Ask your child what steps they might take first or next.  Encourage them to do that step.  Repeat.
• Scribe for your child – model how to write down the equation using labels for all of the numbers.
• If your child is using physical items to solve the problem, help them figure out a way to record that (video/picture/drawing all work) they can even just say "I gathered 84 pennies and then split them one by one into 4 groups" (or whatever it is).
• If your child is truly stuck, do the problem for them, explaining your thinking and what you are doing.  Writing it out using labels and numbers as you go.  If they don't know a computation algorithm you know, don't WORRY! Just explain, "I used my algorithm for solving that multiplication problem…I used multiplicaiton because _______.  (A quick word – "cross multiplication" for solving problems with fractions is not taught until middle school math.  If I send home a problem that you can solve using cross multiplication, know there are other ways to solve it!  See if you can figure out what the cross multiplication is doing to give you a sense of how you might go about helping your child see a pathway.)
• A word about algorithms:  while it's true that we use more algorithms than were taught in schools many years ago, showing your child how you solve a math problem is just fine.  Problem of the Week wouldn't be the ideal time to teach them that algorithm (focus on the problem solving, not the computation) – but showing them how you'd do the computation is fine.  I do have videos of the multiplication and division methods students learn in fourth and fifth grade.  Many fifth graders are also taught the traditional US algorithms for multiplication and division.  Note that your child might not have learned all of these yet.

I DO NOT use Problem of the Week as a formative assessment for children.  I do not use the information I glean from it to give individual students instruction.  Instead, I use it to guide my choice for other problems and to help me what might be helpful for the whole group.

Feedback - I use a rubric to give students feedback on their work as well as write extensive comments.  I use a numerical rubric because I found that when I just put down comments, students often ignored them.  They often felt like it was "all right" even when I had given them a number of things to work on next time.  Thus a number.  It helps them concretize how convincing their argument was for me.  Would I be able to follow it to trust the answer was right?  How well would it have taught someone who was confused how to solve the problem?  If they get a "4" they know they are on the right path and if they read my comments, they will know what they might add to have a more complete answer next time.  (Here is the Download Problem of the Week Rubric I hand out)

It Get's Easier! I had the fifth graders share their initial feelings about problem of the week last year.  They all shared that at first it was hard to label all of their numbers and show their answer clearly.  They also assured the fourth graders that it gets easier!  It is a skill that takes practice and stamina.  It's exhausting to explain your thinking at first (in part because you have to get used to interrogating yourself).  Assure your child that the skills will come more easily the more they do them.

This is Real Math My son is currently in high school and every week he has to do a "Professional Problem" in which he shows every assumption and step that he takes in a way that would convince other mathematicians of the validity of his solution.  It is the Problem of the Week grown up.  Mathematicians spend a small part of their time using numbers to figure things out about our world and a much larger part of the time convincing others of the way they have used those numbers.  Mathematicians are communicators.  Mathematicians are explainers.  (Here's a list of Download What Mathematicians Do)

As your child works on Problem of the Week, those skills are what they are learning.  It's hard work but worth it.

*the link for regular math day  goes to a description of how math works at 4/5, detailing the different parts.  I wrote it several years ago.  "Quick Math" is now Basic Fact Fluency and instead of sheets of practice, students are using flash cards to develop fluency, moving from skip counting to strategies to automacy.  We also do a lot of data handling and measurement during forest school now and it's a significant part of our day on Wednesdays.