diff --git a/mathics/builtin/box/layout.py b/mathics/builtin/box/layout.py
index d198db8b2..d3b7a075b 100644
--- a/mathics/builtin/box/layout.py
+++ b/mathics/builtin/box/layout.py
@@ -390,6 +390,13 @@ class RowBox(BoxExpression):
 
     summary_text = "horizontal arrange of boxes"
 
+    def __init__(self, *args, **kwargs):
+        super().__init__(args, kwargs)
+
+        # TODO Describe why inside row and inside list are needed.
+        self.inside_row = False
+        self.inside_list = False
+
     def __repr__(self):
         return f"RowBox[{self.elements[0].__repr__()}]"
 
diff --git a/mathics/format/render/mathml.py b/mathics/format/render/mathml.py
index 70c641e4c..c1ff6733c 100644
--- a/mathics/format/render/mathml.py
+++ b/mathics/format/render/mathml.py
@@ -1,8 +1,8 @@
 # -*- coding: utf-8 -*-
 """
-Mathics3 Graphics3D box rendering to MathML strings.
+Mathics3 Box rendering to MathML strings.
 
-MathML formatting is usually initiated in Mathics via MathMLForm[].
+MathML rendering is usually initiated via MathMLForm[].
 """
 
 import base64
@@ -169,12 +169,11 @@ def pane_box(box: PaneBox, **options):
 
 
 def fractionbox(box: FractionBox, **options) -> str:
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**options, **box.box_options}
     return "<mfrac>%s %s</mfrac>" % (
-        lookup_conversion_method(box.num, "mathml")(box.num, **options),
-        lookup_conversion_method(box.den, "mathml")(box.den, **options),
+        lookup_conversion_method(box.num, "mathml")(box.num, **child_options),
+        lookup_conversion_method(box.den, "mathml")(box.den, **child_options),
     )
 
 
@@ -204,15 +203,17 @@ def boxes_to_mathml(box, **options):
         raise BoxConstructError
     joined_attrs = " ".join(f'{name}="{value}"' for name, value in attrs.items())
     result = f"<mtable {joined_attrs}>\n"
-    new_box_options = box_options.copy()
-    new_box_options["inside_list"] = True
     for row in items:
         result += "<mtr>"
         if isinstance(row, tuple):
             for item in row:
-                result += f"<mtd {joined_attrs}>{boxes_to_mathml(item, **new_box_options)}</mtd>"
+                item.inside_list = True
+                result += (
+                    f"<mtd {joined_attrs}>{boxes_to_mathml(item, **options)}</mtd>"
+                )
         else:
-            result += f"<mtd {joined_attrs} columnspan={num_fields}>{boxes_to_mathml(row, **new_box_options)}</mtd>"
+            row.inside_list = True
+            result += f"<mtd {joined_attrs} columnspan={num_fields}>{boxes_to_mathml(row, **options)}</mtd>"
         result += "</mtr>\n"
     result += "</mtable>"
     # print(f"gridbox: {result}")
@@ -223,13 +224,14 @@ def boxes_to_mathml(box, **options):
 
 
 def sqrtbox(box: SqrtBox, **options):
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**options, **box.box_options}
     if box.index:
         return "<mroot> %s %s </mroot>" % (
-            lookup_conversion_method(box.radicand, "mathml")(box.radicand, **options),
-            lookup_conversion_method(box.index, "mathml")(box.index, **options),
+            lookup_conversion_method(box.radicand, "mathml")(
+                box.radicand, **child_options
+            ),
+            lookup_conversion_method(box.index, "mathml")(box.index, **child_options),
         )
 
     return "<msqrt> %s </msqrt>" % lookup_conversion_method(box.radicand, "mathml")(
@@ -241,12 +243,11 @@ def sqrtbox(box: SqrtBox, **options):
 
 
 def subscriptbox(box: SubscriptBox, **options):
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**options, **box.box_options}
     return "<msub>%s %s</msub>" % (
-        lookup_conversion_method(box.base, "mathml")(box.base, **options),
-        lookup_conversion_method(box.subindex, "mathml")(box.subindex, **options),
+        lookup_conversion_method(box.base, "mathml")(box.base, **child_options),
+        lookup_conversion_method(box.subindex, "mathml")(box.subindex, **child_options),
     )
 
 
@@ -254,12 +255,13 @@ def subscriptbox(box: SubscriptBox, **options):
 
 
 def superscriptbox(box: SuperscriptBox, **options):
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**options, **box.box_options}
     return "<msup>%s %s</msup>" % (
-        lookup_conversion_method(box.base, "mathml")(box.base, **options),
-        lookup_conversion_method(box.superindex, "mathml")(box.superindex, **options),
+        lookup_conversion_method(box.base, "mathml")(box.base, **child_options),
+        lookup_conversion_method(box.superindex, "mathml")(
+            box.superindex, **child_options
+        ),
     )
 
 
@@ -267,14 +269,15 @@ def superscriptbox(box: SuperscriptBox, **options):
 
 
 def subsuperscriptbox(box: SubsuperscriptBox, **options):
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
-    options["inside_row"] = True
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**box.box_options, **options}
+    box.base.inside_row = box.subindex.inside_row = box.superindex.inside_row = True
     return "<msubsup>%s %s %s</msubsup>" % (
-        lookup_conversion_method(box.base, "mathml")(box.base, **options),
-        lookup_conversion_method(box.subindex, "mathml")(box.subindex, **options),
-        lookup_conversion_method(box.superindex, "mathml")(box.superindex, **options),
+        lookup_conversion_method(box.base, "mathml")(box.base, **child_options),
+        lookup_conversion_method(box.subindex, "mathml")(box.subindex, **child_options),
+        lookup_conversion_method(box.superindex, "mathml")(
+            box.superindex, **child_options
+        ),
     )
 
 
@@ -282,13 +285,10 @@ def subsuperscriptbox(box: SubsuperscriptBox, **options):
 
 
 def rowbox(box: RowBox, **options) -> str:
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
+    # Note: values set in `options` take precedence over `box_options`
+    child_options = {**box.box_options, **options}
     result = []
-    inside_row = options.get("inside_row")
-    # inside_list = options.get('inside_list')
-    options = options.copy()
+    inside_row = box.inside_row
 
     def is_list_interior(content):
         if all(element.get_string_value() == "," for element in content[1::2]):
@@ -309,13 +309,14 @@ def is_list_interior(content):
     if not inside_row and is_list_interior(box.items):
         is_list_row = True
 
-    if is_list_row:
-        options["inside_list"] = True
-    else:
-        options["inside_row"] = True
+    nest_field = "inside_list" if is_list_row else "inside_row"
 
     for element in box.items:
-        result.append(lookup_conversion_method(element, "mathml")(element, **options))
+        if hasattr(element, nest_field):
+            setattr(element, nest_field, True)
+        result.append(
+            lookup_conversion_method(element, "mathml")(element, **child_options)
+        )
 
     # print(f"mrow: {result}")
 
@@ -326,10 +327,8 @@ def is_list_interior(content):
 
 
 def stylebox(box: StyleBox, **options) -> str:
-    _options = box.box_options.copy()
-    _options.update(options)
-    options = _options
-    return lookup_conversion_method(box.boxes, "mathml")(box.boxes, **options)
+    child_options = {**options, **box.box_options}
+    return lookup_conversion_method(box.boxes, "mathml")(box.boxes, **child_options)
 
 
 add_conversion_fn(StyleBox, stylebox)