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Drill or Practice? They Are NOT the Same!


When I was a kid, one of the things I dreaded most was going to the dentist. Even though we were poor, my Mom took my brother and me every six months for a check-up.  Unfortunately, we didn’t have fluoridated water or toothpaste that enhanced our breath, made our teeth whiter, or prevented cavities.  I remember sitting in the waiting room hearing the drill buzzing, humming, and droning while the patient whined or moaned.  Needless to say, I did not find it a pleasant experience.

I am troubled that, as math teachers, we have carried over this idea of drill into the classroom. Math has become a “drill and kill” activity instead of a “drill and thrill” endeavor.  Because of timed tests or practicing math the same way over and over, many students whine and moan when it is math time.  So how can we get student to those “necessary” skills without continually resorting to monotonous drill?

First we must understand the difference between drill and practice.  In math drill refers to repetitive, non-problematic exercises which are designed to improve skills (memorizing basic math facts) or procedures the student already has acquired. It provides:

1)   Increased proficiency with one strategy to a predetermined level of mastery. To be important to learners, the skills built through drill must become the building blocks for more meaningful learning. Used in small doses, drill can be effective and valuable.

2)   A focus on a singular procedure executed the same way as opposed to understanding.  (i.e. lots of similar problems on many worksheets)  I have often wondered why some math teachers assign more than 15 homework problems.  For the student who understands the process, they only need 10-15 problems to demonstrate that.  For students who have no idea what they are doing, they get to practice incorrectly more than 15 times!

Unfortunately, drill also provides:


  3) A false appearance of understanding.  Because a student can add 50 problems in one minute does not mean s/he understands the idea of grouping sets.

 4) A rule orientated view of math.  There is only one way to work a problem, and the reason why is not important!  (Just invert and multiply but never ask the reason why.)

5)   A fear, avoidance, and a general dislike of mathematics. A constant use of math drills often leaves students uninterested.

On the other hand, practice is a series of different problem-based tasks or experiences, learned over numerous class periods, each addressing the same basic ideas. (ex. different ways to multiply)  It provides:

1)   Increased opportunity to develop concepts and make connections to other mathematical ideas.  (i.e. A fraction is a decimal is a percent is a ratio.)

2)   A focus on providing and developing alternative strategies.  My philosophy, which hangs in my classroom, is: “It is better to solve one problem five ways than to solve five problems the same way.”  (George Polya)

3)   A variety of ways to review a math concept.  (ex. games, crosswords, puzzles, group work)

4)   A chance for all students to understand math and to ask why. (Why do we invert and multiply when dividing fractions?) 

5)   An opportunity for all students to participate and explain how they arrived at the answer. Some may draw a picture, others may rely on a number line, or a few may use manipulatives. Good practice provides feedback to the students, and explains ways to get the correct answer.

Let’s look at it this way. A good baseball coach may have his players swing again and again in the batting cage. This drill will help, but by itself it will not make a strong baseball player whereas practicing hitting a ball with a pitcher requires reacting to the different pitches with thought, flexibility, and skill.
I am of the opinion that drill should not be omitted from the math classroom altogether.  Basic math skills should be automatic because being fluent in the basics makes advanced math easier to grasp.  There is a place for drill; however, its use should be kept to situations where the teacher is certain that is the most appropriate form of instruction.  Even though practice is essential, for math it isn't enough. If understanding doesn't come, practice and drill will only leave a student with disjointed skills. If we want to produce strong mathematicians, we must focus on the BIG conceptual ideas through practice in problem-based lessons. We must present ideas in as many forms as we can so that students will go beyond rote drill to insight.

If you are interested in sharing this with your staff, colleagues or parents, check out the FREE power point entitled: Drill vs. Practice. (click on the blue letters) 


A Go Figure Debut for a Reading Specialist Who Is New

Nicole has taught kindergarten and first grade, is a Certified Bilingual Teacher for Spanish in the state of Texas as well as a Master Reading Teacher. During her two years as a reading specialist, she met with reading groups ranging from kindergarten to fifth grades, in conjunction with mentoring and coaching teachers. Her favorite part of being a reading specialist was getting to know and working with so many unique teachers and students. Like most teachers, she loved witnessing the progress of young minds growing and learning so much in just one short school year.

Nicole describes her classroom as a hands-on, differentiated learning environment where children are encouraged to question as much as they are encouraged to learn. She likes planning engaging and differentiated lessons that reach and challenge all learners. Presently, Nicole is a stay-at-home mother of two small children.

Her hobbies are running, cooking, and baking. She especially likes finding yummy healthy recipes. (I could use a few of those!) She likes spending time with her family, taking her children to the park, and visiting her mom, sister, nieces and nephew. When her extended family gets together, she claims that they are all about cooking and eating!!

Nicole’s Teachers Pay Teachers store is called Teacher of 20. It contains a total of 81 resources with four of them being free. 

Her products are perfect for the PreK-2nd classroom, and are mainly for independent centers/work stations in literacy and math. One of those free items is Word Work for October. It features three different activities – a Zig Zag Puzzle, Roll an October Word and Spin and Jump.

Only $9.99

She also has a 330 page CVC Pack of Printables and Literacy Activities. By purchasing this bundle, you save $7.00. Here are just a few of the items included in this resource.
  • 6 student printable books of short vowel words
  • 68 "sound it out" 3 piece puzzles with 2 different accountability sheets
  • 68 zig zag puzzles with 2 accountability sheets
  • 12 color "Spin it!" games and 21 black and white "Spin It!" no-prep printables
  • 4 "Write It!" black and white no-prep printables
  • A word wall for each short vowel
…and much, much more. 

If you are a primary teacher, take some time and check out her store as I am sure Nicole’s quality and reasonably priced products will save you time!

The Pros and Cons of Testing

Tests are here to stay whether we like it or not. As I read various blogs, I am finding more and more teachers who are frustrated over tests and their implications. I am seeing many of my former student teachers leave the teaching profession after only two or three years because of days structured around testing.

High stakes tests have become the “Big Brother” of education, always there watching, waiting, and demanding our time. As preparing for tests, taking pre-tests, reliably filling in bubbles, and then taking the actual assessments skulk into our classroom, something else of value is replaced since there are only so many hours in a day. In my opinion, tests are replacing high quality teaching and much needed programs such as music and art. I have mulled this over for the last few months, and the result is a list of pros and cons regarding tests.

Testing Pros

  1. They help teachers understand what students have learned and what they need to learn.
  2. They give teachers information to use in planning instruction. 
  3. Tests help schools evaluate the effectiveness of their programs. 
  4. They help districts see how their students perform in relation to other students who take the same test. 
  5. The results help administrators and teachers make decisions regarding the curriculum. 
  6. Tests help parents/guardians monitor and understand their child's progress. 
  7. They can help in diagnosing a student's strengths and weaknesses. 
  8. They keep the testing companies in business and the test writers extremely busy. 
  9. Tests give armchair educators and politicians fodder for making laws on something they know little about.  
                                           **The last two are on the sarcastic side.**

Testing Cons
  1. They sort and label very young students, and those labels are nearly impossible to change.
  2. Some tests are biased which, of course, skew the data. 
  3. They are used to assess teachers in inappropriate ways. (high scores = pay incentives?) 
  4. They are used to rank schools and communities. (Those rankings help real estate agents, but it is unclear how they assist teachers or students.) 
  5. They may be regarded as high stakes for teachers and schools, but many parents and students are indifferent or apathetic. 
  6. They dictate or drive the curriculum without regard to the individual children we teach. 
  7. Often, raising the test scores becomes the single most important indicator of overall school improvement. 
  8. Due to the changing landscape of the testing environment, money needed for teachers and the classroom often goes to purchasing updated testing materials. 
  9. Under Federal direction, national testing standards usurp the authority of the state and local school boards. 
  10. Often they are not aligned with the curriculum a district is using; so, curriculum is often changed or narrowed to match the tests. 
Questions That Need to Be Asked
  1. What is the purpose of the test?
  2. How will the results be communicated and used by the district? 
  3. Is the test a reflection of the curriculum that is taught? 
  4. Will the results help teachers be better teachers and give students ways to be better learners?
  5. Does it measure both a student's understanding of concepts as well as the process of getting the answer? 
  6. Is it principally made up of multiple choice questions or does it does it contain any performance based assessment? 
  7. What other means of evaluation does the school use to measure a child's progress? 
  8. Is it worth the time and money?

Putting the Pieces Together

What does it mean to think mathematically?  

It means using math vocabulary, language and symbols to describe or interpret mathematical concepts, procedures and to discover relationships among ideas.  Therefore when a student problem solves, they use previous knowledge, skills, and understanding of concepts to solve a problem.  This process might include formulating problems, applying a variety of strategies, or interpreting results.

What can we do to help our students become better mathematical thinkers?  

We can teach and model problem solving strategies.  We can remember and plan our lessons to involve the three stages of conceptual development: concrete, pictorial, and abstract. We can have the students talk or write about how they got an answer either with the class or with a partner.  We can use writing in the mathematics classroom (such as math journals) to allow the students to practice expository writing and show their understanding.  We can exhibit math word walls and have the students use the glossary in their book to write and define terms. 

We can also create a positive and safe classroom atmosphere for problem solving... 

By being enthusiastic and allowing the students to take risks without consequences.  By emphasizing the process as well as the answer, the students may be willing to try unconventional or different ways to solve the problem.  I always tell my students that there isn't just one right way to get an answer which surprises many of them.  In fact, this is one of the posters that hangs in my classroom.

  
As math teachers, let's continue to emphasize problem solving so that all students will acquire confidence in using mathematics meaningfully. But most of all, let's have fun while we are doing it!

$7.75 on TPT
If you are interested in having a math dictionary for your students, check out A Simple Math Dictionary. It is a 30 page dictionary which uses easy and clear definitions as well as formulas and examples so that students can learn and understand new math words without difficulty or cumbersome language. Most definitions include diagrams and/or illustrations for the visual learner. Over 300 common math terms are organized alphabetically for quick reference.