# Math Tutoring

The key goal of Math Tutoring is to provide problem-solving experiences that build students' understanding of specific math facts and skills.

## Practice in Action

### What Is It?

Math Tutoring involves working with students on specific math skills. This work can take place in ongoing one-on-one or small-group sessions. Tutors, students, and school-day teachers work together to identify skills or areas where students need help, and design activities and review sessions to build specific math skills.

### What Do I Do?

Begin by talking to the school-day teacher to find out what math concepts and skills students are learning, the standards for each grade level, and which students need help. For each student, identify with the school-day teacher the specific math facts or skills that are difficult, examples of problems that the student struggles with, and activities that could help clarify a concept and build understanding. Ask individual students what math skills are difficult for them, what their strengths are, and what kinds of activities they are interested in. Fun activities engage students and increase their desire to learn.

Once specific skills areas have been identified, determine short- and long-term goals. For example, if a younger student is struggling to add two-digit numbers, a short-term goal would be to master equations using base-10 blocks or other manipulatives. A long-term goal would be for the student to be able to add without using manipulatives. Provide regular, positive feedback to encourage students to succeed. At the end of each tutoring session, allow time to discuss what was learned, and what skills and activities require more practice.

The following PDFs may be helpful in organizing and managing your tutoring program:

- Tutoring Receipt (PDF) records a student's participation in a tutoring activity.
- Tutoring Log (PDF) can be used to record information about a student's work over time.

### Why Does It Work?

Research indicates that regular, high-quality one-on-one tutoring may be the most effective afterschool activity for improving academic achievement. One-on-one and small-group mathematics tutoring from well-trained staff allows afterschool programs to target students' individual strengths, weaknesses, and interests by providing direct, diagnostic mathematics instruction and mentoring. This type of tutoring is most effective when tied to the school day, allowing children to practice and reinforce what they are learning in the classroom.

## Planning Your Lesson

Great afterschool lessons start with having a clear intention about who your students are, what they are learning or need to work on, and crafting activities that engage students while supporting their academic growth. Great afterschool lessons also require planning and preparation, as there is a lot of work involved in successfully managing kids, materials, and time.

Below are suggested questions to consider while preparing your afterschool lessons. The questions are grouped into topics that correspond to the Lesson Planning Template. You can print out the template and use it as a worksheet to plan and refine your afterschool lessons, to share lesson ideas with colleagues, or to help in professional development sessions with staff.

- Lesson Planning Template (PDF)
- Lesson Planning Template (Word document)

### Lesson Planning Template Questions

#### Grade Level

What grade level(s) is this lesson geared to?

#### Duration

How long will it take to complete the lesson? One hour? One and a half hours? Will it be divided into two or more parts, over a week, or over several weeks?

#### Learning Goals

What do you want students to learn or be able to do after completing this activity? What skills do you want students to develop or hone? What tasks do they need to accomplish?

#### Materials Needed

List all of the materials needed that will be needed to complete the activity. Include materials that each student will need, as well as materials that students may need to share (such as books or a computer). Also include any materials that students or instructors will need for record keeping or evaluation. Will you need to store materials for future sessions? If so, how will you do this?

#### Preparation

What do you need to do to prepare for this activity? Will you need to gather materials? Will the materials need to be sorted for students or will you assign students to be "materials managers"? Are there any books or instructions that you need to read in order to prepare? Do you need a refresher in a content area? Are there questions you need to develop to help students explore or discuss the activity? Are there props that you need to have assembled in advance of the activity? Do you need to enlist another adult to help run the activity?

Think about how you might divide up groups?who works well together? Which students could assist other peers? What roles will you assign to different members of the group so that each student participates?

Now, think about the Practice that you are basing your lesson on. Reread the Practice. Are there ways in which you need to amend your lesson plan to better address the key goal(s) of the Practice? If this is your first time doing the activity, consider doing a "run through" with friends or colleagues to see what works and what you may need to change. Alternatively, you could ask a colleague to read over your lesson plan and give you feedback and suggestions for revisions.

#### What to Do

Think about the progression of the activity from start to finish. One model that might be usefulâ€”and which was originally developed for science educationâ€”is the 5E's instructional model. Each phrase of the learning sequence can be described using five words that begin with "E": engage, explore, explain, extend, and evaluate. For more information, see the 5E's Instructional Model.

#### Outcomes to Look For

How will you know that students learned what you intended them to learn through this activity? What will be your signs or benchmarks of learning? What questions might you ask to assess their understanding? What, if any, product will they produce?

#### Self-Evaluation

After you conduct the activity, take a few minutes to reflect on what took place. How do you think the lesson went? Are there things that you wish you had done differently? What will you change next time? Would you do this activity again?

### Sample Lessons

### One-on-One Tutoring (K-12)

A student receives tutoring that targets math skills that need support or enrichment activities to enhance math strengths.

### Duration: 15- to 20-minute sessions

### Preparation

- Meet with school-day teachers to identify students who need support or enrichment activities; learn more about the standards and benchmarks at each grade level; and identify specific skill areas, strengths, and learning goals for each student.
- Work with school-day teachers to develop an assessment tool for each student's learning goals. Discuss and design projects and activities that will give students opportunities to practice specific skills, and that will indicate that students are learning.
- Find a quiet, comfortable room where students can focus on the task at hand.

### What to Do

- Begin tutoring sessions with a discussion of the day's goals and make sure that students understand what they are supposed to do. You might ask,
*How will we know you learned this?* - Review the steps involved in that day's session, and work with individual students on each step. Encourage students to ask questions as they move through each problem. Ask questions that encourage students to talk about their approach to the problem.
- Occasionally, teachers request that tutors spend time working through homework during tutoring sessions. Balance homework help with other efforts to keep students interested in and focused on independent learning projects.
- Provide positive feedback to encourage students' success.
- Debrief what was accomplished. Each session should end with the tutor and student discussing what was accomplished and what needs to be done to prepare for the next session. Tutors should be willing to allow students to pursue new questions or ideas if this exploration will contribute to a deeper understanding of the content.

### Outcomes to Look For

- Student engagement and participation
- Progress in identified skill areas
- Increased confidence in identified skill areas
- Answers that reflect an increased understanding of learning goals
- Students communicate about what and how they have learned

### Small-Group Tutoring (K-12)

Students work in small groups on activities that target specific math skills and areas where they need support, or on enrichment activities that enhance their strengths.

### Duration: 20-30 minutes

### Preparation

- Meet with school-day teachers to identify students who need support or enrichment activities; learn more about the standards and benchmarks at each grade level; and identify specific skill areas, strengths, and learning goals for each student.
- Work with school-day teachers to develop an assessment tool for each student's learning goals. Discuss and design projects and activities that will give students opportunities to practice specific skills, and that will indicate that students are learning.
- Group students based on common learning goals and skills.
- Select materials and prepare activities for one-on-one work.

### What to Do

- Define the day's goals and/or skills. Begin tutoring sessions with a discussion of the day's goals. Ensure that the learning goals are ones that students are invested in achieving by asking a question such as,
*How will we know you learned this?* - Group students and monitor both their collaboration skills and learning progress.
- Encourage students to work together; ask questions; and communicate about the activity, how they are approaching the problem, and what they are learning.
- Balance homework help with other efforts to keep students interested in and focused on small-group activities and independent learning goals.
- Provide positive feedback to encourage students' success.
- Debrief what was accomplished. Each session should end with a discussion of what was accomplished and what needs to be done to prepare for the next session. Tutors should be willing to allow students to pursue new questions or ideas if this exploration will contribute to a deeper understanding of the content.

### Outcomes to Look For

- Student engagement and participation
- Progress in identified skill areas
- Increased confidence in identified skill areas
- Answers that reflect an increased understanding of learning goals
- Students communicate about what they have learned and how they learned
- Students work together to problem solve

### Resources

### Technology Tip

Ask Dr. Math is an online forum that provides expert guidance for working math problems and teaching math concepts. You may want to use Dr. Math to prepare for students' math tutoring sessions or go to Ask Dr. Math with students to find help.

If you are working with a group of students, connect to a projector or an electronic whiteboard to help engage students in math and to illustrate math problems better.

Other sites that provide detailed information for working math problems and teaching math concepts include Purplemath and Teacher2Teacher.

For students working on pre-algebra and algebra concepts, Web sites like Algebra Solutions help students practice problems and provide an automated step-by-step solution and answer. These types of sites can be helpful for tutors who may not have a strong knowledge of the skill or concept the student is learning.

### Web Resources

National Library of Virtual Manipulatives for Interactive Mathematics

National Tutoring Association

### Text Resources

Collins, R. C. (1999). *Reading helpers: A handbook for training tutors*: A joint project of the Corporation for National Service, the U.S. Department of Education, and the U.S. Department of Health and Human Services. Available from the National Service Resource Center at:www.nationalserviceresources.org/learns/reading-helpers.

Elbaum, B., Vaughn, S. Hughes, M. T. & Moody, S. M. (2002). How effective are one-to-one tutoring programs in reading for elementary students at risk for reading failure? A meta-analysis of the intervention research. *Journal of Educational Psychology,* 92(4), 605-619.

Fashola, O. S. (1998). *Review of extended-day and after-school programs and their effectiveness* (Report No. 24). Baltimore, MD: Center for Research on the Education of Students Placed at Risk, Johns Hopkins University.

Grossman, J. B., Price, M. L., Fellerath, V., Jucovy, L. Z., Kotloff, L. J., & Raley, R., et al. (2002, June). *Multiple choices after school: Findings from the extended-service schools initiative.* Philadelphia, PA: Public/Private Ventures.

Lauer, P. A., Akiba, M., Wilkerson, S. B., Apthorp, H. S., Snow, D., & Martin-Glenn, M. (2004). *The effectiveness of out-of-school-time strategies in assisting low-achieving students in reading and mathematics: A research synthesis.* Aurora, CO: Mid-continent Research for Education and Learning (McRel).

McComb, E. M., & Scott-Little, C. (2003, March). *After-school programs: Evaluations and outcomes*. Greensboro, NC: SERVE.

Miller, B. M. (2003). *Critical hours: Afterschool programs and educational success*. Brookline, MA: Miller Midzik Research Associates for the Nellie Mae Education Foundation. Retrieved June 15, 2003, from http://www.nmefoundation.org/research/time/critical-hours-after-school-programs-and-education.

O'Connor, S., & McGuire, K. (1998). *Homework assistance & out-of-school time: Filling the need, finding a balance*. Wellesley, MA: The MOST Initiative, National Institute on Out-of-School Time Center for Research on Women.

Office of the Deputy Secretary Planning and Evaluation Service, U.S. Department of Education. (2001).*Evidence that tutoring works*. Retrieved October 30, 2002, from www.ed.gov/inits/americareads/resourcekit/miscdocs/tutorwork.html.

Policy Studies Associates for the US DOE. (1995*) Extending the learning time for disadvantaged students*: *An idea book*. Volume 2, Profiles of Promising Practices. Washington, DC.

Policy Studies Associates for the US DOE. (1995). *Extending the learning time for disadvantaged students: An idea book*. Volume 1, Summary of Promising Practices. Washington, DC.

Potter, J. Blankenship, J., and Carlsmith, L. (1999). *So That Every Child Can Read...America Reads Community Tutoring Partnerships*. Portland, OR: Northwest Regional Educational Laboratories. Retrieved November 1, 2002, from www.eric.ed.gov/.

Powell, A.M., (1997). *Academic Tutoring and Mentoring: A Literature Review*. Retrieved November 6, 2002, from www.library.ca.gov/CRB/97/11/97011.pdf (PDF).

Topping, K., (2000). Tutoring. Retrieved November 6, 2002, fromsmec.curtin.edu.au/local/documents/prac05e.pdf (PDF).

Vega-Rivera, C. & Legowski, M. (2004). *Making tutoring palatable to students.* East Harlem Tutorial Program: New York, NY.st