Keeping it simple
Think Math! FAQ series: How to simplify the use of Think Math! Please share this message with all coaches, math consultants, and Think Math! professional developers.
We’ve been learning several things since publication about ways that Think Math! has become complicated for teachers because of miscommunications about what is, and isn't, "core" to the curriculum. The following points are derived from common difficulties encountered by teachers, and can greatly simplify the use of Think Math!.
TM! provides all you need, but you won’t need all that TM! provides
Think Math! materials provide more than the teacher needs to conduct a successful lesson. In fact, trying to use all of the material will make things harder and reduce your success. The extra material is supplementary, offering options to be used judiciously, but not regularly. The following notes will say what is core, essential, and what is not recommended except in unusual circumstances.
What is core?
The researched core of Think Math! grades 1 through 5 (see special note about kindergarten below) includes only
- a daily Headline Story,
- a daily Skill Practice and Review, and
- a daily 60-minute lesson, which consists of only those items marked with the “clock” icons and lettered "A" through "C" or "D" in the Teach and Practice section of the Teacher Guide.
Core student print-materials include, for each lesson, only
- the Lesson Activity Book (LAB, which is given “clock-icon” time in the 60-minute lesson),
- the associated Practice page (in the Practice book), which can be assigned as homework, or for free time in class or however the teacher wants to do it, and,
- for students who are flying, the associated Extension page (in the Extension Book).
Do not use the Spiral Review at all during the first year. It is not core to the program (not researched with students), and should never compete for time with any core component.
The “1...2...3” structure in the Teacher Guide has been misleading
The “1...2...3” label at the top of the teacher guide pages have made it seem to many teachers (and consultants) that are three steps in the lesson. The only things that are core are
- the Headline Story and Skill Practice and Review, and
- everything with a “clock” icon in the Teach and Practice section.
The section marked "3 Differentiated Instruction," contains additional information to help the teacher, offering optional strategies for modifying parts 1 and 2 for students who are advanced or struggling. It is not a separate step of additional things to do.
Each of the three lesson components—Headline Story, Skill Practice and Review, and Teach and Practice—has its own special purpose, and none can be omitted.
- Teach and Practice develops new concepts, understanding, connections, procedures: it contains the free and guided explorations, the work with manipulatives, and the direct teaching.
- Time: This is a 60-minute lesson daily. The clock icons account for just 50 minutes, because time is lost in transitions. Experience has taught us that if you are having difficulty fitting a lesson into this amount of time, the chances are that part "A" is getting too long. Part A of each lesson should be thought of as a "Launch," an introduction, not a mastery component. Children gain practice from the remaining work in the lesson (other explorations, work with manipulatives, group work, and the LAB) and from the work on the corresponding Practice page.
- Skill Practice and Review is designed for mastery -- it is not the only mastery feature, but it is essential, and without it, skills development (fact competence, for one example) cannot be guaranteed.
- Time: Short, frequent practices are best—from 5-second one-on-one interactions with a single student as you pass the kid’s desk any time of day (in reading, free time, math), to 30 to 90 second whole-group interactions several times a day, as students are transitioning, or standing on line, or... A total of 10 minutes maximum per day, but not less than 4 minutes.
- Headline Story is designed to develop students’ understanding and use of mathematical language -- not specifically vocabulary which comes up more in the Teach and Practice, but the kind of language that appears in word problems. In doing a Headline Story, children are producing the kind of language that they will be consumers of when they face conventional word problems. Headline Stories vary, but the basic principle is that students receive information (in early grades, this might just be pictorial information to describe) but often no question; their task is to figure out what they can say or ask about the problem situation or what they can deduce from the information they’ve been given.
- A typical difficulty that first-time Think Math! teachers have with this feature is that they turn it into its own extended lesson. Spend ten minutes only. Students do not need to solve all problems they can pose; they do not need to analyze the situation in all possible ways. They do need to realize that, almost always, more than one question can be asked/answered from a given set of data. Why is this important? So that when children are reading a word problem, they recognize that it could go in more than one direction, and therefore don’t just skim for numbers and key words and just assume they know what to do; instead, they realize they need to know what question the writers asked.
- Teachers have many ways of teaching Headline Stories. Some write the problem on the board for kids to see and think about as they enter in the morning. Some have them make journal entries on the HS of the day. Some just present them verbally in class for children to discuss. Do include whole-class discussion, even if students are encouraged to read/write/think beforehand. If you do want writing, don’t make it heavy. The big goal is for students to be able to produce the language, and get fluent with a variety of ways of expressing the mathematical ideas out loud: if they can say it, they already have a great leg up on writing it. Writing is both harder and slower, and writing, alone, is less interactive. Discussion is key; writing is extra.
- Time: Ten minutes. Of course, much more can be done with these, but that would take time away from other essential learning.
Don’t underestimate what you know!
It may sound weird, but teachers often forget how enormously much more they know than the children.
Because teachers know what multiplication is, they’ll notice hints of it in first-grade activities, but students are not expected to be learning multiplication. All they need to pay attention to is what is asked of them -- counting, possibly adding, looking for patterns -- and not the additional content that the teacher notices. In a similar way, teachers who know about “base 7” will “see” it in the Eraser Store activities in grade 4. We are not teaching base 7 (no child needs to know base 7) and are writing the numbers in a form that doesn’t even look like base 7 (the numbers of boxes, packages, and erasers are always recorded in some list-like or table-like form). No child will get confused about base-7 arithmetic, because they have no knowledge that base-7 arithmetic even exists. But teachers sometimes see it and wonder why we do that. First grade teachers will also wonder why we do missing addends so early, but that, too, is something that only teachers notice: the problems that we ask kids to do are not hard for them in the form that we are asking them; they become “hard” only if they are presented in the “conventional” missing-addends form, which we do expose them to (but don’t ask them to master), so that they will recognize it when they encounter it in much later lessons.
The important point is that teachers can get confused -- and confuse the children -- not because of what they don't know but precisely because teachers know so much, and don’t realize that Think Math! is making good use of that knowledge, which most curricula do not. Remember, you know a lot: you don’t have to teach everything you know in a lesson; use your knowledge to guide you in teaching what the children need to know, and only what they need to know at this stage, and not at a stage you judge them not yet ready for. Sometimes, they will see a lot in the lesson, and you will want to pursue that. But if they can “do” what the lesson (activities, manipulatives, games, LAB, practice sheet) ask of them, and don’t yet see beyond that, they (and you) are doing fine!
- ↑ Brief answer: to make concrete the idea of packaging and unpackaging, or grouping/regrouping. The reason we choose 7 and not 10 is so that children will have to think a bit, and the reason we choose 7 and not, say, 5 or 4, is so that they get extra practice with what is universally found to be the hardest set of multiplication facts.
The “Chapter Overview” allows teachers to gather materials in advance, but teachers often miss something that is even more essential. Think Math! succeeds in building stronger skills and understanding by having lessons that are highly focused on current learning, but that are conducted in a way that prepares the ground for later lessons. As mentioned in the previous section, teachers can see the content at many levels. The teacher needs to know what is focal and what are the necessary, but non-focal “extras” (approaches that either foreshadow, or prepare the ground for future learning, or that review and help students master prior learning). Two very short readings (each generally less than half a page) go a long way toward simplifying the teacher’s work.
- “About the Chapter” (first page of each Chapter Overview) is short, and is essential reading. Everything else between there and the beginning of Lesson 1 in that chapter may be of some interest/use to the teacher in planning, but is non-essential, and can be skimmed or skipped.
- “Lesson Notes” on the very first page of every lesson contain “About the Lesson” and (often) “About the Mathematics.” These, too, are essential reading.
- Use the Ongoing Assessment suggestions, the “Snapshot Assessment,” and, for documentation and grading, the item called “Chapter Review/Assessment” (the materials in the LAB books). Despite the name "Review/Assessment," those materials are the test, not the review for the test. If teachers are concerned that students have access to these Chapter Review/Assessment tests (because they appear in LABs) before the testing time, they can rip them out of the LABs and distribute them to the students at the proper time.
- In general, do not use the “chapter test” in the Assessment Guide (or on line). That additional testing is not necessary -- Think Math! adequately meets all the purposes of assessment without these additional tests (see assessment and grading) -- and, in many circumstances, has given discouraging underestimates of student learning, which can actually interfere with students' progress toward success on state tests. The materials were meticulously checked for compliance with most state standards, and our in-LAB tests test the appropriate knowledge and skills. Where we have the data, these have been excellent predictors of state-test results.
One core element of the Kindergarten program, the “Morning Time” activity, is buried in the middle of the Chapter Overview material, which many teachers in all grades skip over entirely. It is key to the program. Lesson structure in K is different from lesson structure in the other grades. The short story is that TM! provides all you need, but you won’t need all that TM! Provides. (See Kindergarten for details.)