Ah… Homework

Raise your hand if you remember hating homework as a child …   Raise your hand if you have children and hate it when they have homework … Raise your hand if, as a teacher, you have ever received homework submitted with teardrops on it 🙁     If you haven’t raised your hand yet, you were born under a lucky star, or you have a faulty memory.

On the plus side, homework

• offers a chance for students to independently consolidate skills they learned in a group setting
• builds skills of responsibility and time management

On the negative side, homework

• asks parents to monitor an approach to math they are not familiar with, meaning they may undo learning done in the classroom.
• compromises family and play time because children are too busy with homework.
• might reflect the work of a parent, rather than the thought processes and progress of the child.
• is not backed by solid research, at least at the elementary level, showing its effectiveness in supporting learning.

What to do?

As in many schools, we are expected to give homework, so we had to go back and weigh our thoughts in terms of our BASIC BELIEF:

Math should be taught through understanding, not memorization. In the 21st Century, students will not need speedy calculations skills nearly as much as they will need big-picture thinking, problem-solving skills, and creativity.

So, here are our conclusions, compromises and solutions:

1.  Less is More.  We set a maximum limit of 20 minutes for each math homework assignment, and students have TWO days to complete it (It’s due every other day). This is enough to build  independent organizational skills (one homework benefit). And it allows for other activities – school is important, but the physical, personal and social development of  children is far more important than completing a homework assignment. If a student spends 20 minutes without finishing, they STOP, no penalty.

2.  It’s All About the Thinking. We also do not penalize mistakes on homework. We say, “OK, did you spend a solid 20 minutes, thinking? wondering? Did you get stuck? That’s ok – that’s part of learning.” We then spend the time needed to correct homework in class. By this time, students have skin in the game – they’re interested in finding out how to solve that problem that eluded them alone.

3. Offer Challenge.  Our homework has three levels.

• Level 1 is concrete/pictorial, and solidifies students’ visual understanding of key concepts. (Throughout our fifth grade year, much of Level 1 covers operations with fractions.)  For some students, this is easy and done quickly, giving them more time for Levels 2 and 3. (In the long run, these abstract thinkers still benefit from these small doses of visual underpinning of their conceptual understanding).  For other students, Level 1 is time-consuming, but absolutely essential to their progress. It’s okay to have to draw one or two fraction problems every day for months, if that’s what it takes to internalize understanding. In the mean time, they often excel in concrete investigations done in class, and their confidence grows. These students are usually visual learners, humans who a generation or two ago would have been excluded from grade-level math achievement and soon relegated to dead-end, remedial courses. A huge fraction of our adult population today readily confesses to “not being very good at math”.

• Level 2 is at grade level, and transfers students’ visual understanding to the traditional,  abstract mastery of mathematics. About 90% of our students complete both Levels 1 and 2 on their homework. Students only go on to Level 3 if they have time and interest.
• Level 3 is the challenge level, and is there to give our fast-working students a feeling of struggle and challenge. On a survey yesterday (an exit ticket), several of our fastest students said that Level 3 has not been hard enough, so we’re listening, and will notch it up a little 🙂

Why not just move fast students ahead in the curriculum?

• We realize the importance of higher-level math skills for students who end up going into STEM fields, but their push toward accelerated math should come in high school.  Success in today’s high schools is improved greatly by a solid conceptual basis from K-8, and from the independent ability to doggedly THINK things through. Challenge problems with depth lend a greater mental acuity than speeded-up algorithmic memorization.

With all that in mind, here are our HW assignments 2 – 5 and here is a key to all four of them. HW#2  HW#3  HW#4   HW#5  HW keys 2_5

Enjoy our four consecutive days of investigation lessons, plus one BIG question: “Why the investigations? Are they worth the time invested?”

Continue reading Four Investigations and a Question

We’re hosting Back-to-School night tomorrow. Here are our editable slides that can be either projected or printed out for parents. Break a leg! Continue reading Back-to-School Night

Reminding ourselves of our goals:

1. Higher achievement for all by slowing down the curriculum.
2. Aiming for visualization and conceptual understanding over memorization.
3. Providing challenge for fast learners, by going into more depth.
4. Making math interesting and even fun.

1. Starting With Logic Puzzles

We started the year with several days of logic problems, much like last year  —  see our instructions from last Sept:  WEEK ONE  – A Logic Problem  and WEEK ONE – The Lady and the Tiger ,  and an early classwork/investigation: CW 9_4

Basically, you can use any logic problems – the internet is full of them. Liars and truth-tellers,  brain teasers, riddles. IMPORTANT: Try them yourself, first. They should be easy enough to do, after some head scratching. You’ll run into problems that are too hard or too easy, so caveat emptor. We use a think-pair-share approach to solving these, but other formats would work, too. Continue reading Starting the year: Logic, Fractions and Similes

Welcome Back!    Here we go – Year Two of our blog. (You can read more about us  here.)

We’ve had a great summer, and approach our second year of blogging with the hope that we can improve on what we’re doing.  Of course, that’s the thing about teaching — you never feel like you’ve ‘solved the puzzle’, like you get it completely right. There are way too many moving pieces: needs, circumstances, learning styles, personalities.  But we all keep trying, improving, tweaking.  There is plenty of data documenting the difficulty of our jobs:  here,  here,  and here.

So we’ve promised ourselves that we’d keep teacher morale in mind: Continue reading Our 5th Grade Math Blog — Version 2.0

It’s time to look at recent quizzes and evaluate the progress we’ve made this year. Why is it we teachers remember the slips, the failures, the lessons that didn’t work? We’ll try to be honest with ourselves here, and evaluate our outcomes so far for the year. We’re evaluating the three concepts we feel are VITAL, non-negotiable skills for 5th/6th grade.

I. Fractions

We’re still having students draw their fractions as much as possible. Some students lean towards not wanting to draw – to use their algorithmic shortcuts instead. Which is fine! We do approve of algorithms — they’re excellent shortcuts based on centuries of refinement.  Except that we want BOTH! Algorithmic and conceptual knowledge.    So we’ve switched from computation-style problems to word problems in Level 1 on quizzes. Here’s the outcome:  (we decided to use all female pronouns today) Continue reading Nearing the end… How are we doing? Self-assessment time for us.

Sorry we’ve been incommunicado for a while! In the last month, we’ve had one week of outdoor education (camping), one week of spring break(yay!), one week of standardized testing(no comment) and a week of school-wide theme-based learning(fun).

The trick is not to stress about curriculum 🙂 All those other things matter! If we are measuring LEARNING as our main goal, then each of those (except the standardized testing – yuck!) involves lots of learning.

So this week, we had to start by spending a couple days reviewing the unit we started last month – Angles. Here’s what we believe: Continue reading Problem-solving beats vocabulary

We are surprised every year (re-surprised?) at the most common mistakes fifth graders make around angles.

What’s NOT surprising:

• The difficulty of choosing WHICH of the 2 numbers you encounter on the protractor… Is is 60º or 120º?

What IS surprising

Continue reading Teaching Angles

In 1998, Tom Carpenter and his colleagues documented grades 1–3 students’ use of invented strategies and standard algorithms. The vast majority of students in the study used some invented strategies. The researchers found that students who used invented strategies before learning standard algorithms showed better understanding of place value and properties of operations than those who learned standard algorithms earlier.

We have seen it over and over: a child is tutored early in memorized arithmetic procedures by a well-meaning parent. Continue reading The Case for Withholding Algorithms (For a While!)

Our 8th grade teachers tell us that of the most confusing ideas for students is the difference between linear units (the sides of a rectangle) and quadratic units (the area of a rectangle). Students routinely confuse x,  x-squared, and x-cubed, without realizing what each represents.

This concept SHOULD reach back to a conceptual development in 4th and 5th grade: the idea of area versus perimeter units.

Our solution: We use spaghetti to illustrate the linear units on the sides of a rectangle. (Actually, if available, linguine works better because it’s flatter!) Continue reading Decimal Multiplication – a Visual Approach