Pre-Assessment and Differentiation

As a novice teacher (only in my third year), I keep learning things in my TEACH-NOW program that meet needs I am noticing in my classes.  Like, what do you do when you’ve taught the lesson and given the quiz, and 85% of your class is ready to move on, but 15% really can’t afford to move on?  And 15% of the first group was ready to move on before you even taught the lesson?  What I am learning is that proactive pre-assessment and differentiation are important elements that can prevent the problem I just described.

Pre-assessment activities can be a short quiz or question and answer time with the class before beginning a new unit.   I developed a unit for teaching 6th-graders arithmetic operations involving decimals and made a pre-assessment quiz using Quizlet.  The goal of this assessment is to determine which students already know the material in this lesson, which students are ready to learn this material, and which students may need the lesson broken down into step-by-step directions.

Hypothetically, after the pre-assessment, I determine that I have:

• 5 students who answered most, including the most difficult, of the pre-assessment questions correctly (Group I)
• 12 students who have some knowledge about the topic as shown in their score, but need to develop higher order thinking skills (Group 2), and
• 5 students who appear to have limited knowledge about the topic

After administering the pre-assessment, I can now move forward with the unit by providing the appropriate instruction and activities for the needs of the three different groups (differentiation).

(The concepts are adding, subtracting, multiplying, and dividing decimals and recognizing that decimals are really fractions.)  Students in Group I will focus mainly on complex problems: (problems that involve adding four decimals, or that require adding and subtracting multiple decimals, positive and negative decimals, word problems, and SAT problems involving decimals). Students in Group II will focus mainly on medium level problems (problems with three decimals added, subtracted or multiplied and word problems involving decimals). Students in Group I will focus equally on easy and medium level problems with light exposure to word problems involving decimals. Each lesson has an accompanying quiz, and each day will have entrance/exit tickets to assess each student's progress (See mindmap).

Pre-assessment and differentiation are things I am learning that have the potential of maximizing my effectiveness as a teacher.

Resources

MacMeekin, M. (2017, September 02). 27 Ways To Assess Background Knowledge. Retrieved 

     December 19, 2017, from https://www.teachthought.com/pedagogy/27-ways-assess-background-

     knowledge/

Pendergrass, E. (2013, December). Differentiation: It Starts with Pre-Assessment. Retrieved 
     December 19, 2017, from 
     http://www.ascd.org/publications/educational_leadership/dec13/vol71/num04/
     Differentiation@_It_Starts_with_Pre-Assessment.aspx

Standardized Tests

As I learn about education in the U.S. and around the world through my studies in the TEACH-NOW program, I am at times surprised by how different my experience teaching Middle School Math at a private school is from other schools. Allen Richardson, another student in the TEACH-NOW program wrote the following recently in his blog: “Currently, the District of Columbia Public Schools administers 9 different types of assessments to students in grades K-12, every year. While some are formative, and others are summative, students are continuously bombarded with assessments from the first day of school until the last. . . Of the typical 180-day school year, students spend 72 of those days taking exams; which equates to teachers spending roughly 40% of their instructional time on test preparation. “ That is a lot of testing. (By the way, be sure to read Allen's excellent blog!).

My school is a K-12 school with around 300 students. Grades 3-9 take the Stanford Achievement Test once a year. Testing takes three half days in April. Tenth-graders take the PSAT, and 11th and 12th-grade students take the SAT.

Teachers do not prepare the students for these tests with the exception of daily SAT math questions in high school math classes, and a voluntary high school elective, “SAT Math Prep”. My school is a college preparatory school so it wants the average SAT score to be high and competitive with other local private schools.


As a Middle School Math teacher, I receive copies of the sixth-grade Stanford Achievement Test scores, but not the scores of my seventh-grade or eighth-grade students. I use these scores along with other measurements to determine which sixth-graders will be placed in the advanced math class the following year.

Many schools use standardized tests to evaluate teachers; however, my school doesn’t. I can see that I could keep track of trends in the middle school scores and use them to target weaknesses in my instruction in order to make improvements.

In my state of Georgia, public high schools utilized a high stakes test, the Georgia High School Graduation Test, to determine whether or not a senior graduated.  However, in 2015, a law was passed that allowed students to graduate regardless of their score on this test.  Consequently, this test is no longer taken.

Why the difference between the lack of test stress in my private school versus the abundant test stress at public schools?  The National Center for Education Statistics annually compares the international results of standardized tests.  Nations and states can see who outperforms whom.  Obviously, the educational heavy lifting is done by public schools in America rather than private schools.  Therefore, the better public school students perform the better America will do on the NCES tests.  It is in our best interest as a nation to educate our students to the best of our ability.  And as long as other nations are outperforming us, we can see that we can do better.  Hence, the American way is to test, make adjustments, test, make adjustments, etc.

Perhaps even more importantly, due to the No Child Left Behind Act, standardized test grades were used to determine which U.S. schools were excellent and which were failures.  Money, prestige, and local control were often at stake.  Pressure on public schools to do well on tests was great under NCLB.

Private schools like the one where I teach are not focused on global competition but are more focused on helping students achieve scores on college entrance tests that will allow them to get into the college or university of their choice.

My experience at a private school in the U.S. seems similar to Yanan Hu's experience at an international school in China.  Yanan, another student in the TEACH-NOW program, wrote in a recent blog about the role of standardized testing at her school. Her school is focused on students doing well on Advanced Placement tests but such tests are only high stakes for the students.  Reading her blog will give you insight into international schools and schooling in general in China.

What conclusion(s) do I draw from all this?  Tests should matter and should affect more than simply the future of the test taker.  Well designed tests should be used as part of the criteria for measuring teachers, curriculum, and educational systems.  But with tests come stress so testing must not be continuous.  Neither the private school model nor the D.C. school model seem ideal but more like extremes at opposite ends of the spectrum.

Resources

GA Dept. of Ed. (n.d.).  Georgia High School Graduation Tests (GHSGT). Retrieved

December 12, 2017, from http://www.gadoe.org/Curriculum-Instruction-and-

Assessment/Assessment/Pages/GHSGT.aspx
Hu, Y. (2017, December 08). High Stakes Tests. [Blog post]. Retrieved from
https://yananlz.blogspot.com/2017/12/m6u1a3.html

Richardson, A. (2017, December 11). High Stakes Assessments. [Blog post]. Retrieved
      from https://arichardson2017.wordpress.com/2017/12/11/high-stakes-assessments-
      m6u1a3/

Multicultural Mathematics

I am currently contemplating how to teach Math in a way that includes multicultural appreciation.  A large part of me wants more time on task for my students, since as a whole American students are behind many of their global peers mathematically.  How do I teach this subject in a way that opens young minds to ethnic and cultural diversity but doesn’t take valuable time away from learning math?

One way is to point out what countries are outperforming American students in math to show my students that they can learn better ways of doing things from other cultures.  Coupling this with some best math practices from other countries can give students a greater appreciation for other cultures.  The Common Core Method of Multiplication is actually known as the Chinese Lattice Method of Multiplication. I learned that cultural fact today.  I have previously taught this method to some of my students without the appropriate cultural footnote.

Although it is beyond me at this time, a third way is utilizing culturally diverse word problems would be great.  Currently, my bank of word problems does not possess that diversity.  Over time, I could create word problems that include multicultural names of people and diverse settings.  When combined with the previous ways that I mentioned, multiculturalism could be promoted without taking time off task.

Although I possess a Master’s degree in Intercultural Studies and value diversity, imparting my passion in a math lesson plan is still in the concept stage.  However, I will say that I enjoy using French, Spanish, and Portuguese to compliment my students’ excellent math performances.  Students respond “I don’t know what you just said.”  So I explain.  After a while, older students translate me for new students.  And on days where we don’t have a lot of math to do, I have been known to engage my class in discussions on cultural stereotyping and ethnic jokes and how they affect others.  My students know that I was born in Germany, lived for two and half years in Hawaii, and travel each year outside of the U.S.  So I do impart my love of other cultures to my students, but not necessarily in ways that fit into a math lesson.  But I am learning.

How do I measure my students' growth in cultural competence?  I don’t and I am not sure that I ever will since math is my focus.  But I do take note that my students ask me how to say things in other languages, how and why I learned different languages, and about the countries to which I’ve been.  As long as I spark curiosity in them about other cultures, I feel that to some degree that I am expanding their horizons in this area.

Formative and Summative Assessments

Currently, I am working on a unit on decimals.  I know that I will be teaching sixth-graders how to add, subtract, multiply, and divide multi-digit decimals. Since these are my teaching objectives, I now must develop ways to test my students during and at the end of this unit.

I can give my students an assessment that doesn’t count for much (if any) of their grade, just to see if they are understanding how to apply basic arithmetic operations to decimals.  Such an assessment is known as a formative assessment.  An example of a formative assessment for multiplication of decimals is a multiple choice quiz that only focuses on placing the decimal in the right place in the answer.  If I make the assessment reflect a real-world activity that involves the addition and multiplication of decimals then it would qualify as a performance-based formative assessment.  I think it would be fun to assign my sixth-graders the task of pricing three gift items for a baby shower, a birthday party, or Mother’s/Father’s Day.  Students would take photos of the items and their prices, total the prices, and then multiply the sum by the decimal .07 to calculate the sales tax.  Students would make a poster, powerpoint or document showing the photos, the sum of the prices, the sales tax, and the final total.

Again, this assessment is only formative since it only involves addition and multiplication rather than all four operations.  It cannot be used as a unit test.  Tests that assess the mastery of math skills and count toward the student’s grade would be classified as a summative assessment.  An example of a 20 problem summative test for this unit includes five problems for each operation involving multi-digit decimals.  Now that I have these assessments, I am better prepared to develop lessons on decimals.

What I’ve Learned About Unpacking Standards and Backward Planning

I am extremely grateful for the TEACH-NOW teacher certification program.  In just a few months I have learned more than I dreamed I would.  Each week is a new adventure.  This week I learned about unpacking a standard and backward mapping.  Wow!

I teach at a private school whose curriculum is not aligned with Common Core standards.  Before I began the TEACH-NOW program, I became familiar with the Georgia Department of Education State Standards for Middle School Math. Honestly, I read them but they didn’t mean much to me.  However, now that TEACH-NOW has explained it to me, unpacking the meaning of a standard is quite easy.  A standard states something a student is expected to be able to do.

This standard has the following verbs: add, subtract, multiply, and divide.  The object of all this action is the noun phrase “multi-digit decimals.”  I now understand this standard. It needs at least four main lessons (one for each verb) designed to impart the four skills that will be assessed. For a fuller example of unpacking standards, see my video.

A standard is an example of backward planning.  The standard is the goal that the teacher is pursuing for the students.  Exams or projects will be used to demonstrate that the appropriate skills have been developed.  The lessons and activities will help the students master the skills delineated by the standard.  Standards are simple and powerful.  For a fuller example of the Backward Planning process, see my previous blog.

What was I doing before I learned about unpacking standards and backward planning?  I was lesson-focused.  What lesson does the textbook say to teach next?  What kind of problems does the textbook use?  Based on the answers to these questions, I would teach the next lesson and make quizzes and tests like the textbook problems.

This approach isn’t bad, but it has a potential downside.  The teacher may be unaware of the bigger picture (of sixth-grade math, for example) and may be teaching disjointed, seemingly unrelated lessons.  State standards offer the teacher a map of concepts that a teacher can build lessons around. Yet, as far as I can tell, the state of Georgia has established a sixth-grade math curriculum that has planned every aspect of every lesson for every standard.  Potentially, a teacher could be once again lesson-focused.  However, the lessons always start with a list of state standards to which the wise teacher would do well to pay attention.  With the goal (standard) firmly in mind, the teacher is more likely to help the student reach it.

Now that I understand unpacking standards and backward planning, I feel less like a glorified substitute teacher and more like a professional teacher.  I have a long way to go, but I’m on my way!

Moving Toward Lesson Planning Using Backward Mapping

I am still learning the ropes of teaching.  I usually start with my textbooks, formulate lessons, and then design assessments.  This is a blog on a better practice for creating lessons.

That better way to plan a lesson is to start with the end result in mind, a method known as backward mapping.. “Backward design, also called backward planning or backward mapping, is a process that educators use to design learning experiences and instructional techniques to achieve specific learning goals. Backward design begins with the objectives of a unit or course—what students are expected to learn and be able to do—and then proceeds ‘backward’ to create lessons that achieve those desired goals” (Backward Design Definition, 2013).

The first standard on which I am using this method is a Georgia State Standard for sixth-grade math. It is as follows:

It is easy to find the proficiencies this standard is designed around: adding, subtracting, multiplying, and dividing decimals.  I will focus on three of these.

These proficiencies represent the ends that I am beginning with, the destinations I am seeking my students to reach.  I will know they have reached these goals if they pass assessments of these skills.  Two of my assessments are standard math tests.  The first will test the first two proficiencies, Add/Subtract Decimals Test, and the second will test the third proficiency, Multiplying Decimals Test.  The third assessment will test students ability to recall the rules associated with adding, subtracting, and multiplying decimals.  For example, to add and subtract decimals you must align numbers by their decimals.  To multiply decimals does not require decimal alignment, but instead one must count the total number of decimal places used in the problem and give the answer the same amount of decimal places.  Students will express these rules and give sample problems through one of the following media: a video, a song/poem, or poster.  Here is an example:

Having determined my standard, proficiencies, and assessments, I am ready to create my learning experiences that will move my students toward the goals.

1. Adding Decimals Lesson Outline
1. Whiteboard Lecture
1. Rules for Adding Multi-Digit Decimals
2. Demonstration of Algorithm for Adding Decimals
2. Mini-Whiteboard Challenge: students compete to get the right answer to 20 problems on their mini-white boards.
3. Homework: 10-problem worksheet and making 10 copies of the rules for adding decimals
2. Subtracting Decimals Lesson Outline
1. Video Lesson and Demonstration of Algorithm for Subtracting Decimals
2. Worksheet with 30 problems
3. Homework: None
3. Multiplying Decimals Lesson Outline
1. Whiteboard Lecture
1. Rules for Multiplying Multi-Digit Decimals
2. Demonstration of Algorithm for Multiplying Decimals
2. Large and mini-whiteboard challenge: All students work 12 problems, most on mini-whiteboards while taking turns solving problems on the main whiteboard.
3. Homework: 10-problem worksheet and making 10 copies of the rules for multiplying decimals

Backward planning makes sense.  I look forward to developing these lessons further and implementing them this semester.

Reference

Backward Design Definition. (2013, December 13). Retrieved September 12, 2017, from http://edglossary.org/backward-design/

Improving Behavior

For me, a new teaching year has begun giving me opportunities to experiment with different methods for encouraging excellent academic behavior in my students.  Last year, I simply posted on my class bulletin board a list of names of students who were maintaining an 85 or higher average.  Students who are doing better this year than last year have been requesting that I post the list this year so they can finally see their names on it!  ( And so I will have to do that.)  But I have been trying new things. I divided each class into two to three teams with the highest two or three scoring students as team captains.   The teams gain points from their quizzes and tests scores.  After each test, the team with the most accumulated points gets ice cream at lunch.  I am hoping teammates will encourage and help each other reach higher heights.  Teams also can earn or lose points based on group classroom behavior. Team captains have special privileges such as permission to leave the class for bathroom or water fountain breaks, exemption from having to show their work on homework, and early dismissal if they have completed all their assignments.  So far quiz and test scores are almost entirely in the A range which is a great improvement.

Another way that I am positively reinforcing behavior is taking photos and videos of students and including them in emails to all the parents.  I recently took a photo of seventh-grade students who score 100 on a quiz and sent to all the parent.  Beyond that, I try to praise neat work, perseverance, helpfulness, and self-control verbally.  Last week, at an after school sports event on campus, I had to tell a student that he, as a middle school student, was not allowed to be at the event without his parent.  I instructed him to wait in the late stay classroom until his parent arrived.  The student left immediately and reported to the classroom.  Last year, he would have responded very angrily to such redirection.  So I made sure to tell him later that he responded well and that I was proud of him. I gave him no points or ice cream just well deserved praise.

For academic behavior that is unacceptable, I am traditional in my approach.  I do not accept homework that is messy, or incomplete.  I reward such work with a zero.  The work of students who get C’s or lower on quizzes or tests is examined closely for clues to what is lacking in their understanding.  Then, I take the student aside and reteach them.  Concerned parents are reassured and given details of corrective steps I have taken. And of course, they are given a low grade which shows them they will have to work hard to get their overall grade to improve.

My method for curbing negative non-academic behavior has not changed.  Students who talk while I am lecturing, who respond disrespectfully to me or another student, or engage in “horseplay”, receive a strike for each offense, written by their names on the whiteboard.  Three strikes on one occasion lead to a private conversation with that student about his or her behavior.  Three strikes on another occasion lead to a conversation with the student’s parent about the behavior.  Three strikes on a third occasion lead to a discipline write-up and a meeting with the dean of students who determines the appropriate correction.  Students who have had behavior issues last year are written up after the second occasion.

I generally do not use the three strikes method or disciplinary forms for misbehavior in the lunchroom, however.  Students who are too loud, overly active, who pop bags, throw food, etc. usually get assigned cafeteria clean-up.  If the behavior of an entire table is unacceptable, that table is moved near me for a week or more, so that I can more closely supervise them.  These methods are very effective for curbing negative behavior in the classroom.

With each new year, there are opportunities to improve as a teacher. I am pleased so far with the improvements that I am seeing in my students’ behavior.  Hopefully, you will see success in your corner of education as you experiment with new methods in the areas needing improvement.