用四格表与图形引导讨论篮球队对比：Simpson悖论检验

几何画板及绘图内容加载中，请稍等……

2024-09-25 19:49

所属专题 Kreuztabellen

该范例通过“篮球队A/B谁更强”的情境，引导学习者在同一总体与分组数据可能相互矛盾时做出有依据的判断，重点呈现统计中的Simpson悖论现象。核心数学概念包括：交叉表/四格表的数据读取与解释、分组汇总导致的趋势反转、在矛盾数据下的合理决策与验证。作图与交互实现要点：从构造摘要可见使用了输入框与下拉选择来设置分组或参数（对象如DropDown17/16/15/14/10、textfield/input17/等），并借助几何对象与距离度量进行动态呈现（Point、Distance）；通过Join与Flatten组织生成的几何/文本元素，再用LaTeX输出统计相关的数学表达；同时用If控制条件分支与正确性反馈（inputCorrect14/13/12/11/9/8等）。适合7-8年级及基础统计教学、数据素养训练与课堂讨论活动，用于让学生理解“总体与分组结论可能不一致”的原因。

GeoGebra 命令及参数

SelectedIndex(DropDown17) → input17
SelectedIndex(DropDown16) → input16
SelectedIndex(DropDown15) → input15
Textfield(input14) → Eingabefeld14
Textfield(input13) → Eingabefeld13
Textfield(input12) → Eingabefeld12
Textfield(input11) → Eingabefeld11
SelectedIndex(DropDown10) → input10
Textfield(input9) → Eingabefeld9
Textfield(input8) → Eingabefeld8
Textfield(input7) → Eingabefeld7
Textfield(input6) → Eingabefeld6
SelectedIndex(DropDown5) → input5
Textfield(input4) → Eingabefeld4
Textfield(input3) → Eingabefeld3
Textfield(input2) → Eingabefeld2
Textfield(input1) → Eingabefeld1
Point(Line[A0, yAxis]) → Ay1
Point(Line[A0, xAxis]) → Ax1
Point(Line[Ax1, xAxis]) → Ax2
Distance(Ax1, Ax2) → asizex
Join({Zip[Segment[P, (x(Ax5), y(P))], P, {A0, Ay1, Ay2, Ay3, Ay4}], Zip[Segment[(x(P), y(Ay1)), (x(P), y(Ay4))], P, {A0, Ax1, Ax2, Ax3, Ax4, Ax5}], Zip[Segment[P, (x(P), y(Ay1))], P, {A0, Ax5}]}) → grid1
LaTeX(step, true, true) → Text2
Flatten(Sequence[Sequence[(x(Ax1), y(Ay2)) + (m * (asizex, 0)) + (j * (0, asizey)), m, 0, 3], j, 0, 1]) → listTablePoints1
Point(Line[T3, xAxis]) → T4
If(step < 6, seasonA, seasonB) → season
Zip(Text[(("\textsf\small\bold{" * n) * "}"), P + (absx, absy), true, true], n, {"\textsf{}", (("\textsf\textcolor{6557d2}{" * nameA) * "}"), (("\textsf\textcolor{db6114}{" * nameB) * "\vphantom{g}}")}, m, Sequence[1, 3, 1], P, {Ay1, Ay2, Ay3}) → textTableY1
Zip(Text[(("\textsf\small\bold{" * n) * "}"), P + (1.5 + absx, (1.96 * asizey)), true, true, -0, 1], n, {"\textsf{gewonnene Spiele}", "\textsf{verlorene Spiele}", "\textsf{Spiele insgesamt}", "\textsf{Gewinnquote in %}"}, m, Sequence[1, 4, 1], P, {Ax1, Ax2, Ax3, Ax4}) → textTableX1
Zip(Text[(("\textsf{" * n) * "}"), P + (1.5 + absx, (0.9 * asizey)), true, true, 0, 1], n, {8, 31, 2, 19}, m, Sequence[1, 4, 1], P, Zip[listTablePoints1(k), k, {1, 5, 2, 6}]) → textTableNums1
Zip(Text["\textsf{\%}", P + (2.2 + absx, (0.95 * asizey)), true, true, 0, 1], P, Zip[listTablePoints1(k), k, If[step ≟ 2, {4}, {4, 8}]]) → textTableProzent1
Zip(Text[(("\textsf{" * n) * "}"), P + (1.5 + absx, (0.9 * asizey)), true, true, 0, 1], n, {18, 18, 27, 32}, m, Sequence[1, 4, 1], P, Zip[listTablePoints1(k), k, {1, 5, 2, 6}]) → textTableNums2
Zip(Text[(("\textsf{" * n) * "}"), P + (1.5 + absx, (0.9 * asizey)), true, true, 0, 1], n, {26, 49, 19, 51, 55, 100}, m, Sequence[1, 6, 1], P, Zip[listTablePoints1(k), k, {1, 5, 2, 6, 3, 7}]) → textTableNums3
Join({Sequence[Segment[Corner[4] + (RasterPixMat * ((k * RasterStepXY), 0)), Corner[4] + (RasterPixMat * ((k * RasterStepXY), RasterMaxY))], k, RasterMaxX / RasterStepXY, RasterMaxX / RasterStepXY], Sequence[Segment[Corner[4] + (RasterPixMat * (0, (k * RasterStepXY))), Corner[4] + (RasterPixMat * (RasterMaxX, (k * RasterStepXY)))], k, RasterMaxY / RasterStepXY, RasterMaxY / RasterStepXY]}) → RasterAussen
Element({false, input1 ≟ sol1 ∧ (¬inputCorrect1) ∨ input2 ≟ sol2 ∧ (¬inputCorrect2), input3 ≟ sol3 ∧ (¬inputCorrect3) ∨ input4 ≟ sol4 ∧ (¬inputCorrect4), false, false, input6 ≟ sol6 ∧ (¬inputCorrect6) ∨ input7 ≟ sol7 ∧ (¬inputCorrect7), input8 ≟ sol8 ∧ (¬inputCorrect8) ∨ input9 ≟ sol9 ∧ (¬inputCorrect9), false, false, input11 ≟ sol11 ∧ (¬inputCorrect11) ∨ input12 ≟ sol12 ∧ (¬inputCorrect12), input13 ∈ sol13 ∧ (¬inputCorrect13) ∨ input14 ≟ sol14 ∧ (¬inputCorrect14), false, false, false}, step) → showhintBerechne

AI 绘图提示语参考

画一个篮球比赛数据对比图，展示两支球队在不同条件下的胜负数据和百分比。使用下拉菜单和文本框输入数据，生成一个网格表格，包含球队名称、比赛场次、胜场、负场、总场次和胜率。表格分为两行，分别代表两支球队，并标注百分比。用不同颜色区分两支球队的数据，表格下方绘制坐标轴，并标注坐标轴名称。

以上提示语为根据原始绘图命令整理而来，仅供参考。