Under construction: We add to this list as new questions come in. We are in the process of answering all of these questions. Check often.
Mathematical content and language: How are they developed?
- How does Think Math! develop the following strands:
- Addition and subtraction? See also Number line and Cross number puzzles
- Place value? Response under development.
- Multiplication and division? Response under development.
- Fractions? Response under development.
- Decimals? Coming soon.
- Data analysis? Coming soon.
- Problem solving? See also Headline stories and Problem solving strategies.
- Algebraic thinking and language? Under development. For now, see: number tricks, cross number puzzles, difference of squares.
- Geometric thinking and language? See Area. More coming soon.
- Why does Think Math! put "base 7" before base 10 in 4th grade (chapter 3)? (It doesn't teach base 7, but see details at this link.)
- Will students know their basic facts? Yes! Where are these taught? Coming soon.
- Do students learn the standard algorithms? Yes! Where are these taught? Coming soon.
- Why does Think Math! include "systematic counting," and making systematics lists? Coming soon.
- Why are first graders seeing things that look like algebra? Response under development.
- Why does Think Math! do multiplication in the second grade even before children have mastered subtraction? Response under development.
- Why does Think Math! include logic puzzles in third grade and beyond? Coming soon.
- How does Think Math! help students solve word problems? See Headline stories
- Vocabulary: See Developing mathematical language and Vocabulary and Definition and Glossary
First-year implementation issues
- Keeping it simple: How to keep Think Math! as easy to use as it is intended to be.
- Getting used to Think Math! : For teachers who have not previously taught Think Math!
- Strategies for students who have not had Think Math! the year before
- See also Pacing below.
Alignment with tests and standards
State tests and frameworks
In an effort to assure compatibility with most frameworks and tests, the design process began by compiling and correlating eight sets of standards: National Council of Teachers of Mathematics (NCTM) standards, and the frameworks of California, Florida, Illinois, Massachusetts, New York, North Carolina, and Texas. We designed to meet or exceed these standards at every grade level, and consulted other state frameworks (among them, Michigan, New Jersey, and Ohio) during the writing. The primary organizing principle for lessons and chapters was to achieve a coherent development of mathematical ideas and competence, but we also assured that whatever was needed for the high-stakes state testing occurred before the tests were to be administered. Shortly after the hundredth lesson (certainly before March), the content required for that year's tests should have been learned well. See article on pacing for more about how the year accommodates students and teachers before and after state testing.
Harcourt School Publishers has created or is creating a correlation for each state to show users how Think Math! aligns with their state's frameworks.
NCTM Focal Points
Before we even began designing Think Math!, we derived our model from a prior curriculum (Math Workshop) that was brilliantly focused, and very like what the Focal Points would later call for, long after we started our writing. That original model was also rich, not in all of the ways that PSSM called for, but exactly in that spirit. Second grade did addition and subtraction and place value, and bits of multiplication -- which was started in that grade so that it could be focal in later grades -- but did them in lots of different contexts, so that it didn’t feel like a year-long siege of adding-and-subtracting.
What we ultimately published, though, was less focused than that because all of the state standards, backed up by the threat of their tests, require a lot of little parts (and the risk of becoming the mile-wide curriculum). Under those constraints we had to struggle hard to remain deep. We succeeded because the model from which we started showed how: we do what is focal for the grade throughout, and vary the way we do it in order to provide richness, and to meet state frameworks.
The Focal Points did not exist before we designed the curriculum, so the fact that we correspond so well with the Focal Points is a reflection of how both documents -- Focal Points and Think Math! -- grew from historical wisdom. The focal points listed in Focal Points are not new ideas; and those not-new ideas also informed the design of the original curriculum whose underlying model became the inspiration for Think Math!
Are we focused in exactly the way that Focal Points calls for? Yes. Are we as narrowed as Focal Points are sometimes interpreted as calling for? Not quite. Because if we were, students would fail their state tests.
Structure of the year
Order of topics
- Our district takes topics in a different order. Can I do chapters out of order?
- How can we cover all essential topics before March?
- Our state doesn't require that topic at my grade level. Can I skip those lessons?
- Kids like variety. Can I skip around?
- Do I have to do the Headline Story and Mental Math before the lesson?
- How long should a lesson take?
- Our district limits the time we have available for math.
- If my students have not all mastered the content of a lesson, should I repeat, or should I move on?
- This looks too hard for my kids. The pace seems ambitious. Is this practical?
- Fitting all essentials in before the state test.
- Slower learners
- Gifted learners
- English Language Learners
Teacher's discretion, modifying lessons
- Can I change lesson activities and timing?
- Can I supplement?
- What is the role of manipulatives? Can I do without them? Can I use more?
Distinctiveness of Think Math!
These articles describe the nature, use, and purpose of special features of Think Math!
- number lines
- cross number puzzles
- intersecting lines, arrays, and area for multiplication and division
- silent teaching
- headline stories
- skills practice and review
- mental math
- developing attention, focus, and working memory
Components of Think Math!
- Where is the homework?
Can Think Math! be used in 6th grade?
For the first year of use (that is, for 6th graders who have not been through 5th grade Think Math!), the 5th grade is entirely fine for 6th graders, as long as the pace is a bit different from the fifth grade in the same school, and something extra is done so that the students don’t feel "demoted" by seeing themselves doing what their 5th grade friends are doing. Generally they can go at a faster pace, and take some additional depth or other topics (but not so much that it crowds or confuses the program). That has already been done, and with great success. There is a lot of content in 5th grade, and it is quite appropriate for most 6th graders.
But that can’t be more than a one-year solution, because 5th graders who have already been through the program, even if they could use extra time or review, couldn’t possibly go through the 5th grade program again in 6th grade without the whole experience feeling massively repetitive. It would be the same course two years in a row.
There is a very partial solution for a second year. A common experience of first-time users of Think Math! is that they don’t finish all the chapters (missing two to four chapters at the end of the year, though not ideal, is safe), so 6th graders who have had Think Math! for the first time in 5th grade may have missed some chapters at the end of 5th grade that would be appropriate for 6th grade. In fact, for them, even the end-of-year lessons from the 4th grade might be useful — again, they would not be “beneath” the 6th graders, if handled well — but the combination wouldn’t fill a year, and certainly wouldn't make a coherent and comprehensive program. They could add useful richness, but something else would need to be done.
Pages in category "FAQs"
The following 21 pages are in this category, out of 21 total.