https://www.youtube.com/watch?v=jFPqnFxyEek
Transformations on the coordinate plane.
Friday, November 5, 2021
Pre-Algebra Q2 Temperature change from minus to more minus
The temperature on a winter Monday morning is -15.4 degrees according to a digital thermometer. The temperature drops a little more each day. Four days later, it has dropped 20% from the Monday morning reading of -15.4. What is that temperature four days later after the 20% drop, measured to the tenth of a degree?
Explain in writing how you completed the task. What did you do and in what order did you do it?
After you have completed your written explanation, pick a new starting temperature for a new problem. Please choose a negative temperature between -1 and -9. Then choose a percentage drop of between 20% and 40%. After you set up the new problem, solve it yourself and be prepared to explain your problem and answer.
Something to think about...
If we started at +10 degrees and had a 50% drop, would you expect the new temperature to be +5 degrees? If we started at -10 degrees and had a 50% drop, would you expect the new temperature to be -5 or -15? Why?
An answer and explanation for Q2 will be published in another post soon.
Pre-Algebra A1 Answer for filling the tank
The cost of gas for a truck is $3.59. The gas tank holds 28.2 gallons when empty, but it is 1/5 full now. How much will it cost to fill the tank?
Answer: $80.99 (80.9904 rounded to cents)
The tank needs 22.56 gallons to become full (80% of 28.2, because 1/5 is 20%). Now multiply $3.59 times 22.56.
An alternate method would be to calculate the cost of a full tank, then subtract 20%. The full tank ($3.59 times 28.2) is $101.238; do not round in the middle of the task. 20% of $101.238 is $20.2476. Subtract $20.2476 from $101.238 and you get $80.9904.
Tuesday, June 1, 2021
Pre-Algebra Q1 Calculating the cost of filling the tank.
The cost of gas for a truck is $3.59. The gas tank holds 28.2 gallons when empty, but it is 1/5 full now. How much will it cost to fill the tank?
Explain in writing how you completed the task. What did you do and in what order did you do it?
After you have written the explanation of your work process, think about this question. Can you see another, different way to complete the problem; a different process? If you can, write out that explanation, step by step. Once you have done that, try the second way and see if you get the same answer.
Finally, if you did any rounding of decimals in your work process, think about how that might have impacted your accuracy. It is usually best to not do any rounding until the end.
An answer and explanation will be published in another post soon.
Friday, January 22, 2021
K12 Education needed a paradigm change before the pandemic
Click here for a two page summary of my thoughts on K12 education:
https://drive.google.com/file/d/10Q3OEnenFQPSyrbWWbf64M7v3qhpWKdP/view
Click here for my manuscript of about 100 pages, plus appendices:
https://drive.google.com/file/d/11acKOGaw-V9iscQHX6cc0fqAoqqydtff/view
Wednesday, December 2, 2020
Escaping the K12 Doom Loop
Click the link to open a pdf version of my book: Escaping the K12 Doom Loop.
https://drive.google.com/file/d/11acKOGaw-V9iscQHX6cc0fqAoqqydtff/view?usp=sharing
K12 education has never worked well for most Americans, especially those who come from poverty or distressed households. The paradigm of moving students along by age cohort, regardless of skill mastery, puts students at an increasing disadvantage as time marches on. Many types of school reform have come and gone, but the doom loop of the conveyor belt has never been adequately addressed. My book details faults of the conveyor belt and offers alternatives. You will find embedded links within the narrative that will take you to supporting materials. I encourage you to follow the links as you go.
Comments are encouraged. Thank you!
Saturday, February 1, 2020
Teach Children to Learn
K12 education in America is preparing children for tests, but not teaching children how to learn. Additionally, in spite of the testing and reporting of scores, students move to the next grade level or course regardless of test result or course grade. Students are assigned grade levels according to age cohort and moved along as a cohort until at least the freshman year of high school. From kindergarten to ninth grade students move from year to year, even when they fail to learn the curriculum, fail to learn how to learn, and fail the standardized tests. Not only do the failing students suffer, but the vast majority of students who appear to pass the courses and pass the tests are not mastering the curriculum. They move on with the age cohort and begin each year with content knowledge gaps, gaps that widen with each successive year.
The system is designed to move students along curriculum content knowledge paths, but it fails to teach the skills required for learning. Students are tested for content knowledge, then, no matter the test score, the students are moved on to the next level. Teacher preparation programs and licensing criteria focus on teacher content knowledge and content transfer through lesson planning. Teacher lesson planning preparation assumes too much. It assumes a reasonably motivated student. It assumes a student who wants to learn and earn good grades. It assumes a student with adequate prior skills and knowledge. It assumes that students are in stable family situations that support learning and promote good behavior.
With the exception of early elementary pre-service teachers, teacher preparation and licensing programs give only cursory attention to how students learn and how teachers prepare, assess, and reteach students learner skills. This creates a common reality: Students move into fourth grade (as an example) with learner skill gaps, content knowledge gaps, and a teacher whose priority is the fourth grade content that will be tested at year end. Yes, that teacher understands that some students will need some extra support, but the demands of teaching the class the fourth grade curriculum will soon create a pace that leaves some, perhaps many, students behind. A teacher steeped in content knowledge and trained in content delivery will often neglect the learning skill needs of students; not because they want to, but because the environment and their training steers their focus away from learner skill development and toward content knowledge gaps.
An example that assumes a good student in fourth grade with stable life inside and outside school might illustrate the point. The teacher assesses math readiness of the student early in the year and determines that the student is at grade level having scored well on the standard assessment of third grade content. In fourth grade, the curriculum guide places multiplication of two digit numbers before division using a two digit divisor (for example 175 divided by 25). The student in question struggles with two digit multiplication as evidenced by classwork. The teacher provides support in the form of corrections of the student’s work, models of worked out solutions for other examples, and additional remedial two digit multiplication problems. A quiz on two digit multiplication is given to the class before the first lesson on division using two digit divisors. The student scores 80% on the multiplication quiz, but struggles with the two digit divisor classwork as he did with the two digit multiplication classwork.
Continuing with this example, the teacher provides support in the form of corrections to the student’s division work, models of worked out solutions, and additional remedial division problems. Recognizing that the student still has not mastered the two digit multiplication as evidenced by the 80% quiz score, the teacher also provides the student some two digit multiplication problems after doing some one on one reteaching. The teacher also reaches back to the fundamentals of division with the student by working through some division problems using single digit divisors (for example 175 divided by 5) before reviewing the two digit division problems with the student. As we can see, in addition to teaching the daily lessons according to the pacing guide, the teacher is providing individual content skills coaching to the students. In this example, the student entered fourth grade on grade level in content knowledge and scored 80% on the two digit multiplication quiz.
Assuming the teacher is providing similar content readiness feedback and support to all students, what’s missing? Attention to learner skills and development of student agency are both missing from the teacher’s approach. This is the norm. This is how the teacher was trained. This is how administrators guide teachers to help struggling students. This is the approach parents expect from teachers. The teacher is focusing on the student’s gaps in content knowledge and content skills. The teacher is not addressing learner skills. What are learner skills? Learner skills are applicable to any content and grow over time into life skills. Examples of learner skills that might be appropriate for a fourth grade student include: persistence, avoiding distractions, striving for accuracy, applying prior knowledge, questioning, explaining process steps being used, and various other self-discipline or self-monitoring skills.
The system is designed to move students along curriculum content knowledge paths, but it fails to teach the skills required for learning. Students are tested for content knowledge, then, no matter the test score, the students are moved on to the next level. Teacher preparation programs and licensing criteria focus on teacher content knowledge and content transfer through lesson planning. Teacher lesson planning preparation assumes too much. It assumes a reasonably motivated student. It assumes a student who wants to learn and earn good grades. It assumes a student with adequate prior skills and knowledge. It assumes that students are in stable family situations that support learning and promote good behavior.
With the exception of early elementary pre-service teachers, teacher preparation and licensing programs give only cursory attention to how students learn and how teachers prepare, assess, and reteach students learner skills. This creates a common reality: Students move into fourth grade (as an example) with learner skill gaps, content knowledge gaps, and a teacher whose priority is the fourth grade content that will be tested at year end. Yes, that teacher understands that some students will need some extra support, but the demands of teaching the class the fourth grade curriculum will soon create a pace that leaves some, perhaps many, students behind. A teacher steeped in content knowledge and trained in content delivery will often neglect the learning skill needs of students; not because they want to, but because the environment and their training steers their focus away from learner skill development and toward content knowledge gaps.
An example that assumes a good student in fourth grade with stable life inside and outside school might illustrate the point. The teacher assesses math readiness of the student early in the year and determines that the student is at grade level having scored well on the standard assessment of third grade content. In fourth grade, the curriculum guide places multiplication of two digit numbers before division using a two digit divisor (for example 175 divided by 25). The student in question struggles with two digit multiplication as evidenced by classwork. The teacher provides support in the form of corrections of the student’s work, models of worked out solutions for other examples, and additional remedial two digit multiplication problems. A quiz on two digit multiplication is given to the class before the first lesson on division using two digit divisors. The student scores 80% on the multiplication quiz, but struggles with the two digit divisor classwork as he did with the two digit multiplication classwork.
Continuing with this example, the teacher provides support in the form of corrections to the student’s division work, models of worked out solutions, and additional remedial division problems. Recognizing that the student still has not mastered the two digit multiplication as evidenced by the 80% quiz score, the teacher also provides the student some two digit multiplication problems after doing some one on one reteaching. The teacher also reaches back to the fundamentals of division with the student by working through some division problems using single digit divisors (for example 175 divided by 5) before reviewing the two digit division problems with the student. As we can see, in addition to teaching the daily lessons according to the pacing guide, the teacher is providing individual content skills coaching to the students. In this example, the student entered fourth grade on grade level in content knowledge and scored 80% on the two digit multiplication quiz.
Assuming the teacher is providing similar content readiness feedback and support to all students, what’s missing? Attention to learner skills and development of student agency are both missing from the teacher’s approach. This is the norm. This is how the teacher was trained. This is how administrators guide teachers to help struggling students. This is the approach parents expect from teachers. The teacher is focusing on the student’s gaps in content knowledge and content skills. The teacher is not addressing learner skills. What are learner skills? Learner skills are applicable to any content and grow over time into life skills. Examples of learner skills that might be appropriate for a fourth grade student include: persistence, avoiding distractions, striving for accuracy, applying prior knowledge, questioning, explaining process steps being used, and various other self-discipline or self-monitoring skills.
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