How to Teach Knowing Mathematics

Q: What do I need for teaching Knowing Mathematics?

A: To teach Knowing Mathematics you don't need anything more than what you have now. We are sure that you have enough mathematical content knowledge to teach this program. In fact, we expect that your knowledge of elementary mathematics as well as your knowledge about students' learning will grow through teaching Knowing Mathematics. If there is any one thing that we would like you to have before you begin this program, it would be that you care about your students and their learning. As long as you believe that you are a teacher who cares about your students' learning, work with them on this program and we believe that you will succeed!

Q: How do I select students?

A: Any student in Grades 4 through 6 who is below grade level can benefit from this program. No special test is needed for selecting students. Spend two to three weeks in early fall to observe your class, and you will have a sense of who in your class needs to be accelerated in their mathematics learning. One typical feature may be that they don't know addition and subtraction facts, and/or multiplication and division tables well. Some students may seem to know facts reasonably well, but don't know how to apply their knowledge to other mathematical situations. Any student who you think may have trouble keeping up with your regular class can be involved in this program.

However, try to have a good group dynamic — make sure you have enough students with a positive attitude in the group. If you have too many students who don't even care about their mathematics, try to stagger sessions and take only a few at a time.

Q: How do I plan a lesson?

A: Lesson planning for Knowing Mathematics is simple: Before you teach the book, read this Overview carefully and scan the whole book. Before you teach a particular unit, read the Unit Overview and the teaching support for all of the lessons in the unit carefully. Find interesting features of the lessons, figure out how the unit is organized, and why it might work. Before you teach a particular lesson, carefully read the lesson support at least two times. Work all of the exercises. You don't need to prepare a lot of materials, but you need to be very familiar with the content and organization of the lesson that you are teaching.

Q: What should I keep in mind when I am teaching Knowing Mathematics?

A: Two things. First, pacing. Research has revealed that successful intervention lessons are systematic, structured, and fast paced. The instruction in Knowing Mathematics is systematic and structured. Pacing is in your hands. Pacing is what keeps the program intensive so it will eventually work. If you see students struggling, encourage them, but don't slow down your pace.

The second thing we would like you to keep in mind is that you must demand that every student do the work. Being demanding is a way to show your respect for students and your belief that they can learn. The program is carefully written to match the developmental level of fourth- through sixth-graders. If students can't meet the goal for a certain lesson, for example, to memorize the multiplication table for that day, after all the activities and exercises in your class, what they need is only a reasonable extra effort. On the same day, ask the students seriously to make this effort and they will make it.

Q: What do I do with students' work?

A: Correct every single problem every day. Correct all the work that students have done in class before they leave. We have strategically placed pauses throughout the Exercise sets and these are perfect places to stop and correct student work before you go ahead. Correct any homework you may assign before the class starts. Correcting students' work does not merely give students feedback about what they have learned. Even more important, it shows that you care about your students and appreciate their efforts.

Q: How do I assess my students' progress?

A: The assessment in Knowing Mathematics is both informative as well as summative, providing opportunities to teach as well as to review. It is extremely important when working with low at-risk students to monitor students' learning progress all the time; don't wait until grading their quiz or examination. The Teacher's Guide will help you in this on-going monitoring of students' progress.

Assessment of Learning Assessment for Learning
Unit Quizzes
End of lesson:

Reflection and Discussion questions
Return to the Title of the Lesson
Exit Exam
Entry Exam
Mathematical Conversations:

Discussion Points
Guided Practice
Independent Exercises:

End of Lesson:
Reflection and Discussion questions

Q: What support do my students need from their families?

A: Some of the exercise sets are lengthy and you may need to ask students to do some sections as homework. Parents and guardians need to support students in doing this work outside of class, making sure that students have a time and a place in which to do it.



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