As you know, Husband is a 5th grade teacher (9- and 10-year-olds). What you might not know is that he teaches in a Dual Language Immersion (DLI) school, which has been a major factor in who, how, and what he teaches--and it has posed some very frustrating problems.
In our DLI schools, students need to be enrolled in the dual-language classes by the beginning of 2nd grade (our schools have kindergarten 4- and 5-year-olds, 1st grade 5- and 6-year-olds, and 2nd grade 6- and 7-year-olds) or they cannot be enrolled. The DLI classes spend half their day in English instruction classes and half their day in the other language instruction with a fluent dual-language or native language speaker as a teacher.
For the DLI kids, it's an awesome program. The students in DLI most often have attentive and proactive parents, so the students are generally better behaved, better educated, and expect more of themselves. The class sizes are small as well, with about 15-20 students per class. As the students age and move up in grade, some students move out of the area or drop out of DLI classes, which decreases the class size permanently because, after the beginning of 2nd grade, no new students can enter the DLI program. With small class sizes and generally brighter students, each student enjoys more individualized attention, and the teachers have a good experience and are easily able to manage and teach the classes. Parents with DLI students are very vocal about keeping the DLI programs in the schools.
For non-DLI kids, however, the program has led to some negative unintended consequences. Students who move in after the start of 2nd grade or who drop out of the DLI program are shunted to the regular classes. With all the growth in our area, regular classes have become huge--often with 30+ students and counting as more apartment complexes and single-family homes are built. Limited numbers of teachers in each grade also means that students with behavior issues or special needs can't be easily distributed across classes to make classroom management easier. Brighter students must try to learn in an environment that is increasingly disorderly and chaotic despite teachers' efforts, and students who struggle are at an even greater disadvantage. There is no remedy for this situation except to hire more teachers, but both district budgets for teacher salaries and the lack of physical space to accommodate more classes almost always prevents this.
The result of all of this is that our burg's elementary schools are now offering a two-tiered education experience: one small group gets an excellent education and becomes fluent in another language; and the other, much larger, group suffers in all areas. Case in point: Husband's DLI class a couple years ago passed as proficient 60% or more of the students in all areas of standardized testing. Last year, his massive non-DLI class that he tried very hard to teach in the same way as the DLI kids passed as proficient only 19% at the most in standardized testing. You can imagine his frustration.
Knowing that they needed to change something, Husband suggested to his two fellow 5th grade non-DLI colleagues that they try a junior high/high school model approach in their grade, where students move to different classrooms for different subjects rather than stay in one classroom with one teacher all day. The three non-DLI 5th grade teachers each chose two specialty areas that they would teach. Husband chose to teach math and social studies. The other two teachers divided up science, language arts, writing, and reading between them. That way, each of them could concentrate and focus better at making lesson plans for two subjects rather than trying to create effective lesson plans in all subjects. Additionally, each of them would only have each class for one-third of the day rather than all day.
Over the summer, Husband did hours and hours of research on his own time. His math teaching model was obviously not working for non-DLI students, so he honed in on a different approach--a pretty radical approach compared to what has become the norm in public schools. This new approach is based on the research of Peter Liljedahl in his book, Building Thinking Classrooms. The goal is to teach students how to think and problem solve rather than show them a formula, have them work through it and then do some homework.
Liljedahl's research in how to structure a classroom and how to teach students to problem solve set all your normal public school education experience on its head. Husband really liked Liljedahl's method and set up his classroom to reflect it.
First, he did away with a front and back of the classroom. Where students normally sit at desks and look to the front for teacher instruction, Husband made groups of three desks each surrounding a table in the center of the room from which students could collect the supplies they would need for each lesson. Around the perimeter, Husband attached vertical whiteboards and dry erase markers to the walls.
Each day as the students come in, they are seated randomly in groups. They really only use the desks to drop their stuff as their groups are then assigned to a set of whiteboards. Husband then presents them with a problem, and the students have to work together to solve it. No one is allowed to go and sit at a desk. Each of the three participants of each group must participate in some way, whether writing on the board or making suggestions for the solution. The groups can look at other groups' whiteboards or ask other groups about their possible solutions. Husband patrols the room to help guide the students by either giving hints or asking questions to help the students move toward the solution. He never tells them directly if they are on the right path or if they have the correct answer; instead, he challenges them to prove to him that they have found the best solution by walking him through their thought processes.
One of the questions he posed is this: a farmer needs to build a fence as cheaply as possible around his garden in order to keep animals out. The fence must be three feet wider than the 14' by 11' garden to allow movement around the garden plot, and it must include a three-foot gate. The farmer can buy any combination of 10' fence panels, 2' panels, or 1' panels in order to achieve this (the prices of the panels were given to the students).
The other day, Husband handed me one of the problems he had developed and wanted me to work through it to see if he had done it well enough to be understandable. The concept he is trying to teach is place value. Then he watched me intently while I worked through the solution, which was nerve-wracking because I am really not sure if I'm smarter than a 5th grader. Fortunately, I was able to come up with the correct solution. Then he handed me an extension to the problem, and, again, I managed to come up with the correct solution. I am inordinately pleased by this. I still feel a little rush of pleasure when I think about how I was able to solve it--and I'm in my 50s. I have never been good at math. Imagine how great a 5th grader will feel when they work with their group members to figure it out! Imagine those kids now feeling like maybe they're smart enough to do math, which, for many, is a breaking point.
The Jewelry Heist
A jewelry store had a break-in and lost some inventory. They lost between $1 million and $2 million dollars' worth of stones.
1. They lost twice as many emeralds as they did cubic zirconias.
2. They lost the same number of rubies as they did amethyst stones, and the combined amount adds up to make a double-digit number.
3. For one type of stone, only one was stolen.
4. The number of stolen agates plus the number of stolen diamonds is equal to 6, but more agates were stolen than diamonds.
5. When the total dollars lost was calculated, the last three digits added up to make 12, and the first three digits added up to make 8.
6. Each stone type had fewer than 7 stones stolen.
7. The lowest-value stone had three times the number stolen than the highest-value stone.
Values:
Cubic Zirconias: $1 each
Agates: $10 each
Amethysts: $100 each
Emeralds: $1000 each
Rubies: $10,000 each
Diamonds: $100,000 each
Pink diamonds: $1,000,000 each
Find out how many of each stone was stolen. What value does each stone category have? What is the total value?
(I put the answer at the bottom of this post. Don't peek until you work through this! If I can do it, you can do it.)
Once you have solved that, here's the extension:
When the jewels were found, the pink diamond had been cut in half, and its value was now only half as much as originally. Half of the emeralds were still missing, and all the rubies had vanished. Of the remaining jewels, each had lost 1 of their original number.
How many of each stone is left? What value does each stone category now have? What is the total value?
I am very proud of Husband. School started a couple weeks ago, and he has been helping the students become familiar and comfortable with this method of problem solving and thinking. This means he is on his feet walking around to help student groups all day, but he feels it is worth it.
My oldest grandson, Tyler, is a new kindergartner. He loves school. Husband takes him in the morning, and Siân drives the younger two boys to pick him up in the afternoon. Because of parent demand, the school had to create four all-day kindergartens, and Siân was a little worried about that at first, but Tyler seems to be thriving.
Answers:
The Jewelry Heist. Number of stolen stones: 3 cubic zirconias, 4 agates, 5 amethysts, 6 emeralds, 5 rubies, 2 diamonds, and 1 pink diamond were stolen. The value of each stolen stone category: $3 cubic zirconias; $40 agates; $500 amethysts; $6000 emeralds; $50,000 rubies; $200,000 diamonds; $1,000,000 pink diamonds. Total value: $1,256,543.
Extension: Number of stones left: 2 cubic zirconias; 3 agates; 4 amethysts; 1 diamond; 0 rubies; 3 emeralds; and 0 pink diamonds. Value of each stone category: $500,000 pink diamonds; $3000 emeralds; $0 rubies; $100,000 diamonds; $400 amethysts; $30 agates; and $2 cubic zirconias. Total value: $603,432
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